Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$g(x)=|x|$ on $(-\infty, 0)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$m(x)=x^{3}$ on $(0, \infty)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$f(x)=x$ on $(-\infty, \infty)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$k(x)=-x^{2}$ on $(0, \infty)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$p(x)=\sqrt[3]{x}$ on $(-\infty, 0)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$h(x)=x^{2}$ on $(-\infty, 0)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$r(x)=4-\sqrt{x}$ on $(0, \infty)$

Dwijendra R.

Numerade Educator

Inspect the graph of the function to determine whether it is increasing or decreasing on the given interval.

$g(x)=|x|$ on $(0, \infty)$

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the intervals on which $f(x)$ is increasing.

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the intervals on which $f(x)$ is decreasing.

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the intervals on which $f^{\prime}(x)<0$

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the intervals on which $f^{\prime}(x)>0 .$

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the $x$ coordinates of the points where $f^{\prime}(x)=0$.

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the $x$ coordinates of the points where $f^{\prime}(x)$ does not exist.

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the $x$ coordinates of the points where $f(x)$ has a local maximum.

Dwijendra R.

Numerade Educator

Refer to the following graph of $y=f(x)$

Identify the $x$ coordinates of the points where $f(x)$ has a local minimum.

Dwijendra R.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty)$ and has critical numbers at $x=a, b, c,$ and $d$. Use the sign chart for $f^{\prime}(x)$ to determine whether $f$ has a local maximum, a local minimum, or neither at each critical number.

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Give the local extrema off and match the graph off with one of the sign charts $a$ - $h$ in the figure on page $250 .$

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Dwijendra R.

Numerade Educator

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.

$f(x)=x^{3}-12 x+8$

Dwijendra R.

Numerade Educator

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.

$f(x)=x^{3}-27 x+30$

Dwijendra R.

Numerade Educator

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.

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

Dwijendra R.

Numerade Educator

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.

$f(x)=\frac{5}{x-4}$

Dwijendra R.

Numerade Educator

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.

$f(x)=|x|$

Dwijendra R.

Numerade Educator

Find $\left(\right.$ A) $f^{\prime}(x),($ B) the partition numbers for $f^{\prime},$ and $($ C) the critical numbers of $f$.

$f(x)=|x+3|$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

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

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=-3 x^{2}-12 x$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=-2 x^{2}-16 x-25$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=-3 x^{2}+12 x-5$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=x^{3}+4 x-5$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=-x^{3}-4 x+8$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=2 x^{3}-3 x^{2}-36 x$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=-2 x^{3}+3 x^{2}+120 x$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=3 x^{4}-4 x^{3}+5$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=x^{4}+2 x^{3}+5$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=(x-1) e^{-x}$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=x \ln x-x$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

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

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=\left(x^{2}-9\right)^{2 / 3}$

Dwijendra R.

Numerade Educator

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=x^{4}-4 x^{3}+9 x$

Dwijendra R.

Numerade Educator

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=x^{4}+5 x^{3}-15 x$

Dwijendra R.

Numerade Educator

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=x \ln x-(x-2)$

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Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

$f(x)=e^{-x}-3 x^{2}$

Dwijendra R.

Numerade Educator

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

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

Dwijendra R.

Numerade Educator

Use a graphing calculator to approximate the critical numbers of $f(x)$ to two decimal places. Find the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema.

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

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

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

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

$f(x)=2 x^{2}-8 x+9$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

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

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

$f(x)=x^{3}-12 x+2$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

$f(x)=10-12 x+6 x^{2}-x^{3}$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

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

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

$f(x)=x^{4}-18 x^{2}$

Dwijendra R.

Numerade Educator

Find the intervals on which $f(x)$ is increasing and the intervals on which $f(x)$ is decreasing. Then sketch the graph. Add horizontal tangent lines.

$f(x)=-x^{4}+50 x^{2}$

Dwijendra R.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

$f(-2)=4, f(0)=0, f(2)=-4$

$f^{\prime}(-2)=0, f^{\prime}(0)=0, f^{\prime}(2)=0$

$f^{\prime}(x)>0$ on $(-\infty,-2)$ and $(2, \infty)$

$f^{\prime}(x)<0$ on (-2,0) and (0,2)

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

$f(-2)=-1, f(0)=0, f(2)=1$

$f^{\prime}(-2)=0, f^{\prime}(2)=0$

$f^{\prime}(x)>0$ on $(-\infty,-2),(-2,2),$ and $(2, \infty)$

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

$f(-1)=2, f(0)=0, f(1)=-2 ;$

$f^{\prime}(-1)=0, f^{\prime}(1)=0, f^{\prime}(0)$ is not defined;

$f^{\prime}(x)>0$ on $(-\infty,-1)$ and $(1, \infty)$

$f^{\prime}(x)<0$ on (-1,0) and (0,1)

Aman G.

Numerade Educator

$f(x)$ is continuous on $(-\infty, \infty) .$ Use the given information to sketch the graph off.

$f(-1)=2, f(0)=0, f(1)=2$

$f^{\prime}(-1)=0, f^{\prime}(1)=0, f^{\prime}(0)$ is not defined;

$f^{\prime}(x)>0$ on $(-\infty,-1)$ and (0,1)

$f^{\prime}(x)<0$ on (-1,0) and $(1, \infty)$

Aman G.

Numerade Educator

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.

$f_{1}$

Aman G.

Numerade Educator

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.

$f_{2}$

Aman G.

Numerade Educator

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.

$f_{3}$

Aman G.

Numerade Educator

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.

$f_{4}$

Aman G.

Numerade Educator

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.

$f_{5}$

Aman G.

Numerade Educator

Involve functions $f_{1}-f_{6}$ and their derivatives, $g_{1}-g_{6} .$ Use the graphs shown in figures (A) and ( B) to match each function $f_{i}$ with its derivative $g_{j}$.

$f_{6}$

Aman G.

Numerade Educator

Use the given graph of $y=f^{\prime}(x)$ to find the intervals on which $f$ is increasing, the intervals on which $f$ is decreasing, and the x coordinates of the local extrema off. Sketch a possible graph of $y=f(x)$.

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Use the given graph of $y=f(x)$ to find the intervals on which $f^{\prime}(x)>0,$ the intervals on which $f^{\prime}(x)<0,$ and the values of $x$ for which $f^{\prime}(x)=0 .$ Sketch a possible graph of $y=f^{\prime}(x)$.

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Aman G.

Numerade Educator

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.

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

Aman G.

Numerade Educator

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.

$f(x)=\frac{9}{x}+x$

Aman G.

Numerade Educator

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.

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

Aman G.

Numerade Educator

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.

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

Aman G.

Numerade Educator

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.

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

Aman G.

Numerade Educator

Find the critical numbers, the intervals on which $f(x)$ is increasing, the intervals on which $f(x)$ is decreasing, and the local extrema. Do not graph.

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

Aman G.

Numerade Educator

The graph of the total profit $P(x)$ (in dollars) from the sale of $x$ cordless electric screwdrivers is shown in the figure.

(A) Write a brief description of the graph of the marginal profit function $y=P^{\prime}(x)$, including a discussion of any $x$ intercepts.

(B) Sketch a possible graph of $y=P^{\prime}(x)$.

Aman G.

Numerade Educator

The graph of the total revenue $R(x)$ (in dollars) from the sale of $x$ cordless electric screwdrivers is shown in the figure.

(A) Write a brief description of the graph of the marginal revenue function $y=R^{\prime}(x),$ including a discussion of any $x$ intercepts.

(B) Sketch a possible graph of $y=R^{\prime}(x)$.

Aman G.

Numerade Educator

The figure approximates the rate of change of the price of bacon over a 70 -month period, where $B(t)$ is the price of a pound of sliced bacon (in dollars) and $t$ is time (in months).

(A) Write a brief description of the graph of $y=B(t)$, including a discussion of any local extrema.

(B) Sketch a possible graph of $y=B(t)$.

Aman G.

Numerade Educator

The figure approximates the rate of change of the price of eggs over a 70 -month period, where $E(t)$ is the price of a dozen eggs (in dollars) and $t$ is time (in months).

(A) Write a brief description of the graph of $y=E(t)$, including a discussion of any local extrema.

(B) Sketch a possible graph of $y=E(t)$.

Aman G.

Numerade Educator

A manufacturer incurs the following costs in producing $x$ water ski vests in one day, for $0<x<150$ : fixed costs, $\$ 320 ;$ unit production cost, $\$ 20$ per vest; equipment maintenance and repairs, $0.05 x^{2}$ dollars. So, the cost of manufacturing $x$ vests in one day is given by

$$

C(x)=0.05 x^{2}+20 x+320 \quad 0<x<150

$$

(A) What is the average $\operatorname{cost} \bar{C}(x)$ per vest if $x$ vests are produced in one day?

(B) Find the critical numbers of $\bar{C}(x),$ the intervals on which the average cost per vest is decreasing, the intervals on which the average cost per vest is increasing, and the local extrema. Do not graph.

Aman G.

Numerade Educator

A manufacturer incurs the following costs in producing $x$ rain jackets in one day for $0<x<200$ : fixed costs, $\$ 450 ;$ unit production cost, $\$ 30$ per jacket; equipment maintenance and repairs, $0.08 x^{2}$ dollars.

(A) What is the average cost $\bar{C}(x)$ per jacket if $x$ jackets are produced in one day?

(B) Find the critical numbers of $\bar{C}(x),$ the intervals on which the average cost per jacket is decreasing, the intervals on which the average cost per jacket is increasing, and the local extrema. Do not graph.

Aman G.

Numerade Educator

A drug is injected into the bloodstream of a patient through the right arm. The drug concentration in the bloodstream of the left arm $t$ hours after the injection is approximated by

$$

C(t)=\frac{0.28 t}{t^{2}+4} \quad 0<t<24

$$

Find the critical numbers of $C(t),$ the intervals on which the drug concentration is increasing, the intervals on which the concentration of the drug is decreasing, and the local extrema. Do not graph.

Aman G.

Numerade Educator

The concentration $C(t),$ in milligrams per cubic centimeter, of a particular drug in a patient's bloodstream is given by

$$

C(t)=\frac{0.3 t}{t^{2}+6 t+9} \quad 0<t<12

$$

where $t$ is the number of hours after the drug is taken orally. Find the critical numbers of $C(t),$ the intervals on which the drug concentration is increasing, the intervals on which the drug concentration is decreasing, and the local extrema. Do not graph.

Aman G.

Numerade Educator