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Problem 44

a. Identify the function's local extreme values i…

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Problem 44

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.
$$
g(x)=-x^{2}-6 x-9, \quad-4 \leq x<\infty
$$
Problem 45

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.
$$
f(t)=12 t-t^{3}, \quad-3 \leq t<\infty
$$
Problem 46

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.
$$
f(t)=t^{3}-3 t^{2}, \quad-\infty< t \leq 3
$$
Problem 47

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.
$$
h(x)=\frac{x^{3}}{3}-2 x^{2}+4 x, \quad 0 \leq x<\infty
$$
Problem 48

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.
$$
k(x)=x^{3}+3 x^{2}+3 x+1, \quad-\infty<x \leq 0
$$
Runpeng L.
University of California, Riverside
Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72
Problem 43

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.
$$
g(x)=x^{2}-4 x+4, \quad 1 \leq x<\infty
$$

Answer

See the graph

Chapter 4
Applications of Derivatives
Section 3
Monotonic Functions and the First Derivative Test
Thomas Calculus

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Video Transcript

and the function, which is G X, defined as X squared minus four x does war. So for part Elvis problem, we need to check the extreme that local extreme values. To do that, we first take the derivative of the function, which is to X minus four, and we let this rip him to be zero we can't solve for X, though axes to that it means G too. He's a local extreme value. But for part B, we need to identify whether this extreme value local stream batteries Absolute. Now we call that shape of this function is a rebel A and the only route is too. So the function should be looked like be like this and the domain is from one to infinity. So let's say this one. And until infinity we have the increasing function from 2 to 20. So have to will be our absolute minimum. So after is absolute or cheat you sorry. Due to its absent

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