2. The function ƒ is continuous on the closed interval [-3,3] such that f(-3) =4 and f(3)=1. The functions f'(x) and f"(x) have the properties given in the table below. -3
2. The function ƒ is continuous on the closed interval [-3,3] such that f(-3) =4 and f(3)=1. The functions f'(x) and f"(x) have the properties given in the table below. -3
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![2. The function ƒ is continuous on the closed interval [-3,3] such that f(-3)=4 and f(3)=1. The functions f '(x)
and f"(x) have the properties given in the table below.
-3<x<-1
x = -1
-1<x<1
x =1
1<x<3
Fails to
f (x)
Positive
Negative
Negative
Exist
Fails to
f "(x)
Positive
Positive
Negative
Exist
(a) At what value of x does f(x) attain its absolute minimum value on the closed interval –3<x<3? At what
value of x does f(x) attain its absolute maximum value on the closed interval -3 <x<3? Show the
analysis that leads to your answer.
(b) Find the x-coordinate of each point of inflection of the graph of f(x). Justify your answer.
(c) Sketch a possible graph of f(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F757bcf29-d7db-48c9-98ad-64e62642f099%2F50c61ca1-151b-461b-ba57-16f14e2d538e%2Fh69pc9_processed.png&w=3840&q=75)
Transcribed Image Text:2. The function ƒ is continuous on the closed interval [-3,3] such that f(-3)=4 and f(3)=1. The functions f '(x)
and f"(x) have the properties given in the table below.
-3<x<-1
x = -1
-1<x<1
x =1
1<x<3
Fails to
f (x)
Positive
Negative
Negative
Exist
Fails to
f "(x)
Positive
Positive
Negative
Exist
(a) At what value of x does f(x) attain its absolute minimum value on the closed interval –3<x<3? At what
value of x does f(x) attain its absolute maximum value on the closed interval -3 <x<3? Show the
analysis that leads to your answer.
(b) Find the x-coordinate of each point of inflection of the graph of f(x). Justify your answer.
(c) Sketch a possible graph of f(x).
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