   Chapter 4.3, Problem 35E ### 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 continuous function f is shown.(a) On what intervals is f increasing? Decreasing?(b) At what values of x does f have a local maximum? Local minimum?(c) On what intervals is f concave upward? Concave downward?(d) State the x-coordinate(s) of the point(s) of inflection.(e) Assuming that f(0) = 0, sketch a graph of f. (a)

To determine

To find: The intervals of the given graph f where the function f is increasing and the interval where f is decreasing.

Explanation

The function f(x) is increasing if the first derivative of the given function is positive. From the given graph, it is observed that f(x)>0 on the intervals (0,2),(4,6),(8,) . Therefore, f(x) is increasing on (0,2),(4,6),(8,) .

The function f(x) is decreasing if the first derivative of the given function is negative

(b)

To determine

To find: The value of x where the function f have local maximum and the value where f have local minimum.

(c)

To determine

To find: The intervals of the given graph f where the function f is concave upward and the interval where f is concave downward.

(d)

To determine

To find: The x-coordinate of the inflection point.

(e)

To determine

To sketch: The graph of f if f(0)=0 .

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