4. Let f be a function defined on the closed interval (-2, 8] with f(0) -n. The graph of f', the derivative of ƒ, consists of a semicircle and t segments, as shown in the figure below. 2(0,2) (-2,0) (2,0) (8,0) 4 6. (4,-2) a. Find the maximum value of function f on the interval -2 SxS8. Show your work and justify your answer. b. Find the minimum value of function f on the interval -2SxS8. Show your work and justify your answer.
4. Let f be a function defined on the closed interval (-2, 8] with f(0) -n. The graph of f', the derivative of ƒ, consists of a semicircle and t segments, as shown in the figure below. 2(0,2) (-2,0) (2,0) (8,0) 4 6. (4,-2) a. Find the maximum value of function f on the interval -2 SxS8. Show your work and justify your answer. b. Find the minimum value of function f on the interval -2SxS8. Show your work and justify your answer.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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only part A and part B please
![4. Let f be a function defined on the closed interval (-2, 8] with f(0) - n. The graph of f', the derivative of f, consists of a semicirele and tw
segments, as shown in the figure below.
2|(0,2)
(-2,0)/
(2,0)
(8,0)
6
(4,-2)
a. Find the mnaximum value of function f on the interval -2 <xS8. Show your work and justify your answer.
b. Find the minimum value of function f on the interval -2SxS8. Show your work and justify your answer.
c. Use the linear approximation of function f at the point (0, n) to estimate the value of f(0.1).
d. Is your estimate larger or smaller than f(0.1)? Explain your reasoning.
because this point is the only value where f'(x)
changes
from increasing to
at2 X=2
from positive to negative.. f
goes
de creasing, whìch is the only maximum from -24x8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12916fce-3fd6-4ec0-a7ea-5fe6627d780b%2F5255f8a8-c643-4e3f-9144-64dae0f54024%2F6t80c4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Let f be a function defined on the closed interval (-2, 8] with f(0) - n. The graph of f', the derivative of f, consists of a semicirele and tw
segments, as shown in the figure below.
2|(0,2)
(-2,0)/
(2,0)
(8,0)
6
(4,-2)
a. Find the mnaximum value of function f on the interval -2 <xS8. Show your work and justify your answer.
b. Find the minimum value of function f on the interval -2SxS8. Show your work and justify your answer.
c. Use the linear approximation of function f at the point (0, n) to estimate the value of f(0.1).
d. Is your estimate larger or smaller than f(0.1)? Explain your reasoning.
because this point is the only value where f'(x)
changes
from increasing to
at2 X=2
from positive to negative.. f
goes
de creasing, whìch is the only maximum from -24x8
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