5. The graph of f is shown below. Let g(x) = ª* f(t) dt 3- 2 -1- 0 1 2 3 4 5 /6 7 8 9 10 11 थी -1 -2 --3 36 (a) Find the average value of ƒ on the interval [0, 12] if g(12) = ㅠ (b) At what value of x on the interval [0, 12] does g(x) (not f(x)) reach its absolute maximum? Briefly explain your reasoning. 12
5. The graph of f is shown below. Let g(x) = ª* f(t) dt 3- 2 -1- 0 1 2 3 4 5 /6 7 8 9 10 11 थी -1 -2 --3 36 (a) Find the average value of ƒ on the interval [0, 12] if g(12) = ㅠ (b) At what value of x on the interval [0, 12] does g(x) (not f(x)) reach its absolute maximum? Briefly explain your reasoning. 12
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![**5. The graph of \( f \) is shown below. Let \( g(x) = \int_{0}^{x} f(t) \, dt \)**
A graph is displayed with the x-axis ranging from 0 to 12 and the y-axis ranging from -4 to 4. The graph of the function \( f \) shows a curve that fluctuates up and down within this range.
(a) **Find the average value of \( f \) on the interval [0, 12] if \( g(12) = -\frac{36}{\pi} \).**
(b) **At what value of \( x \) on the interval [0, 12] does \( g(x) \) (not \( f(x) \)) reach its absolute maximum? Briefly explain your reasoning.**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F953e3ae3-1a36-4eca-a542-ddeb8c6ae72a%2Fdbeec0d0-7126-4a33-b6d3-9cb856871e2a%2Fugyhqxs_processed.png&w=3840&q=75)
Transcribed Image Text:**5. The graph of \( f \) is shown below. Let \( g(x) = \int_{0}^{x} f(t) \, dt \)**
A graph is displayed with the x-axis ranging from 0 to 12 and the y-axis ranging from -4 to 4. The graph of the function \( f \) shows a curve that fluctuates up and down within this range.
(a) **Find the average value of \( f \) on the interval [0, 12] if \( g(12) = -\frac{36}{\pi} \).**
(b) **At what value of \( x \) on the interval [0, 12] does \( g(x) \) (not \( f(x) \)) reach its absolute maximum? Briefly explain your reasoning.**
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