   Chapter 4.3, Problem 5E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The graph of the derivative f′ of a function f is shown.(a) On what intervals is f increasing or decreasing?(b) At what values of x does f have a local maximum or minimum? (a)

To determine

To find: The intervals on which f is increasing or decreasing by using the graph of the derivative function.

Explanation

Definition used:

The function f is said to be increasing on the interval (a,b) if the first derivative of that function is greater than 0 on that interval.

The function f is said to be decreasing on the interval (a,b) if the first derivative of that function is lesser than 0 on that interval.

Description:

From the given graph, it is observed that the value of f(x) lies above the x-axis on the interval (1,5) and so is greater than 0 for any x on that interval and from the given graph, it is also observed that the value of f(x) lies below the x-axis on the interval (0,1) and (5,6) and so is lesser than 0 for any x on those intervals

(b)

To determine

To find: The values of x in which the function f(x) have a local maximum or minimum.

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