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a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$k(x)=x^{2 / 3}\left(x^{2}-4\right)$$

a. Identify the function's local extreme values in the given domain, and say where they occur.b. Which of the extreme values, if any, are absolute?c. Support your findings with a graphing calculator or computer grapher.$$f(x)=2 x-x^{2}, \quad-\infty<x \leq 2$$

a. Identify the function's local extreme values in the given domain, and say where they occur.b. Which of the extreme values, if any, are absolute?c. Support your findings with a graphing calculator or computer grapher.$$f(x)=(x+1)^{2}, \quad-\infty<x \leq 0$$

a. Identify the function's local extreme values in the given domain, and say where they occur.b. Which of the extreme values, if any, are absolute?c. Support your findings with a graphing calculator or computer grapher.$$g(x)=x^{2}-4 x+4, \quad 1 \leq x<\infty$$

a. Identify the function's local extreme values in the given domain, and say where they occur.b. Which of the extreme values, if any, are absolute?c. Support your findings with a graphing calculator or computer grapher.$$g(x)=-x^{2}-6 x-9, \quad-4 \leq x<\infty$$

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a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$h(x)=x^{1 / 3}\left(x^{2}-4\right)$$

$-\frac{2}{\sqrt{7}}$

No transcript available

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$h(r)=(r+7)^{3}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(x)=\frac{x^{3}}{3 x^{2}+1}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(\theta)=3 \theta^{2}-4 \theta^{3}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$f(\theta)=3 \theta^{2}-4 \theta^{3}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(\theta)=6 \theta-\theta^{3}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(r)=3 r^{3}+16 r$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(x)=x^{4}-8 x^{2}+16$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(t)=-3 t^{2}+9 t+5$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$h(x)=-x^{3}+2 x^{2}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$f(x)=x^{4}-8 x^{2}+16$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(t)=-t^{2}-3 t+3$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$K(t)=15 t^{3}-t^{5}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(x)=x^{2} \sqrt{5-x}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$f(\theta)=6 \theta-\theta^{3}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$H(t)=\frac{3}{2} t^{4}-t^{6}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(x)=x \sqrt{8-x^{2}}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(x)=x^{4}-4 x^{3}+4 x^{2}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$h(x)=-x^{3}+2 x^{2}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(x)=x^{2 / 3}(x+5)$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$g(t)=-3 t^{2}+9 t+5$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$g(t)=-t^{2}-3 t+3$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$g(x)=x^{4}-4 x^{3}+4 x^{2}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$K(t)=15 t^{3}-t^{5}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$H(t)=\frac{3}{2} t^{4}-t^{6}$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$g(x)=4 \sqrt{x}-x^{2}+3$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(x)=\frac{x^{2}-3}{x-2}, \quad x \neq 2$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$h(x)=2 x^{3}-18 x$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\sqrt{x^{2}+10}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\frac{x+5}{x+2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=\sqrt{x^{2}+1}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\frac{(x+7)}{(x+2)}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\sqrt{x^{2}+6}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\frac{x+2}{x+1}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=x^{4}+4 x^{3}+4 x^{2}+1$$

a. Find the open intervals on which the function is increasing and decreasing.b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$f(x)=x-6 \sqrt{x-1}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=x^{2 / 3}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.b. Identify the function's local extreme values, if any, saying where they occur.$$h(x)=2 x^{3}-18 x$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\ln \frac{5 x^{2}+4}{x^{2}+1}$$

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.Graph

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=x^{2} 2^{-x}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=x^{16 / 17}-x^{33 / 17}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\frac{x+3}{x-4}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$f(x)=x^{4}+16 x^{3}+64 x^{2}+4$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=(x+6)^{4 / 5}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=(x+1)^{4 / 5}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=x^{6 / 7}-x^{13 / 7}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=x \sqrt{9-x^{2}}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=-5 x-14$$

For each of the following functions, use a graphing calculator to find the open intervals where $f(x)$ is (a) increasing, or (b) decreasing.$$f(x)=\ln \left(x^{2}+1\right)-x^{0.3}$$

In Exercises 75 and $76 :$a. Find the open intervals on which the function is increasingand decreasing.b. Identify the function's local and absolute extreme values, ifany, saying where they occur.$$g(x)=x^{2}-2 x-4 \ln x$$

In Exercises 75 and $76 :$a. Find the open intervals on which the function is increasingand decreasing.b. Identify the function's local and absolute extreme values, ifany, saying where they occur.$$g(x)=x(\ln x)^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=-3 x-16$$

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.GRAPH CANNOT COPY

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=2.9+5.6 x-1.3 x^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=2.3+5.6 x-1.3 x^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=1.1-0.3 x-0.3 x^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where the function is decreasing. (Refer to Section 5.1 )$$y=\sin x$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=x^{1 / 3}+x^{4 / 3}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=-3 x+6$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$f(x)=\frac{2}{3} x^{3}-x^{2}-4 x+2$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.$$y=x^{2 / 3}-x^{5 / 3}$$

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## Recommended Questions

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.$$

k(x)=x^{2 / 3}\left(x^{2}-4\right)

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

h(r)=(r+7)^{3}

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(x)=\frac{x^{3}}{3 x^{2}+1}

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(\theta)=3 \theta^{2}-4 \theta^{3}

$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$f(\theta)=3 \theta^{2}-4 \theta^{3}$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(\theta)=6 \theta-\theta^{3}

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(r)=3 r^{3}+16 r

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(x)=x^{4}-8 x^{2}+16

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(t)=-3 t^{2}+9 t+5

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

h(x)=-x^{3}+2 x^{2}

$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$f(x)=x^{4}-8 x^{2}+16$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(t)=-t^{2}-3 t+3

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

K(t)=15 t^{3}-t^{5}

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(x)=x^{2} \sqrt{5-x}

$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$f(\theta)=6 \theta-\theta^{3}$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

H(t)=\frac{3}{2} t^{4}-t^{6}

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(x)=x \sqrt{8-x^{2}}

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(x)=x^{4}-4 x^{3}+4 x^{2}

$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$h(x)=-x^{3}+2 x^{2}$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(x)=x^{2 / 3}(x+5)

$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$g(t)=-3 t^{2}+9 t+5$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$g(t)=-t^{2}-3 t+3$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$g(x)=x^{4}-4 x^{3}+4 x^{2}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$K(t)=15 t^{3}-t^{5}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$H(t)=\frac{3}{2} t^{4}-t^{6}$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

g(x)=4 \sqrt{x}-x^{2}+3

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(x)=\frac{x^{2}-3}{x-2}, \quad x \neq 2

$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

h(x)=2 x^{3}-18 x

$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\sqrt{x^{2}+10}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\frac{x+5}{x+2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=\sqrt{x^{2}+1}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\frac{(x+7)}{(x+2)}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\sqrt{x^{2}+6}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\frac{x+2}{x+1}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{4}+4 x^{3}+4 x^{2}+1$$

a. Find the open intervals on which the function is increasing and decreasing.

b. Identify the function's local and absolute extreme values, if any, saying where they occur.

$$

f(x)=x-6 \sqrt{x-1}

$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{2 / 3}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{2 / 3}$$

a. Find the open intervals on which the function is increasing and those on which it is decreasing.

b. Identify the function's local extreme values, if any, saying where they occur.

$$h(x)=2 x^{3}-18 x$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\ln \frac{5 x^{2}+4}{x^{2}+1}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\ln \frac{5 x^{2}+4}{x^{2}+1}$$

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.

Graph

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.

Graph

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.

Graph

Graph

Graph

Graph

Graph

Graph

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{2} 2^{-x}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{2} 2^{-x}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{16 / 17}-x^{33 / 17}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\frac{x+3}{x-4}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$f(x)=x^{4}+16 x^{3}+64 x^{2}+4$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=(x+6)^{4 / 5}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=(x+1)^{4 / 5}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=x^{6 / 7}-x^{13 / 7}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=x \sqrt{9-x^{2}}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=-5 x-14$$

For each of the following functions, use a graphing calculator to find the open intervals where $f(x)$ is (a) increasing, or (b) decreasing.

$$f(x)=\ln \left(x^{2}+1\right)-x^{0.3}$$

In Exercises 75 and $76 :$

a. Find the open intervals on which the function is increasing

and decreasing.

b. Identify the function's local and absolute extreme values, if

any, saying where they occur.

$$g(x)=x^{2}-2 x-4 \ln x$$

In Exercises 75 and $76 :$

a. Find the open intervals on which the function is increasing

and decreasing.

b. Identify the function's local and absolute extreme values, if

any, saying where they occur.

$$g(x)=x(\ln x)^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=-3 x-16$$

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.

GRAPH CANNOT COPY

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.

GRAPH CANNOT COPY

Find the open intervals where the functions graphed as follows are (a) increasing, or (b) decreasing.

GRAPH CANNOT COPY

GRAPH CANNOT COPY

GRAPH CANNOT COPY

GRAPH CANNOT COPY

GRAPH CANNOT COPY

GRAPH CANNOT COPY

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=2.9+5.6 x-1.3 x^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=2.3+5.6 x-1.3 x^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=1.1-0.3 x-0.3 x^{2}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where the function is decreasing. (Refer to Section 5.1 )

$$y=\sin x$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=x^{1 / 3}+x^{4 / 3}$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=-3 x+6$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\frac{2}{3} x^{3}-x^{2}-4 x+2$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$f(x)=\frac{2}{3} x^{3}-x^{2}-4 x+2$$

For each function, find (a) the critical numbers; (b) the open intervals where the function is increasing; and (c) the open intervals where it is decreasing.

$$y=x^{2 / 3}-x^{5 / 3}$$