   Chapter 4.3, Problem 24E ### 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

# Sketch the graph of a function that satisfies all of the given conditions.(a) f′(x) < 0 and f″(x) < 0 for all x(b) f′(x) > 0 and f″(x) > 0 for all x

(a)

To determine

To sketch: The graph of the function which satisfies the conditions that f(x)<0 and f(x)<0 for all x.

Explanation

Graph:

Since the first derivative of the function f(x) is negative, the function f(x) is always decreasing.

That is, if f(x)<0 , then f(x) is decreasing.

Since the second derivative of the function f(x) is negative, the function f(x) is always concave downward

(b)

To determine

To sketch: The graph of the function which satisfy the following conditions that f(x)>0 and f(x)>0 for all x.

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 