y = f'(x) The graph of the derivative is shown to the right. Which graph below best illustrates the graph of its original function, f(x), and why? A D

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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y = f'(x)
The graph of the derivative is shown to the right.
Which graph below best illustrates the graph of its original function, f(x), and why?
A
D
Transcribed Image Text:y = f'(x) The graph of the derivative is shown to the right. Which graph below best illustrates the graph of its original function, f(x), and why? A D
Expert Solution
Step 1

Given that

Calculus homework question answer, step 1, image 1

From this graph we see that there is a local maximum at some point. 

It means f"(c)=0 for some c. 

And f"(x) < 0 for all x > c (because after x=c, f"(x) is decreasing )

And f" (x) >0 for all x< c (because before x=c, f'(x) is increasing )

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