   Chapter 5.3, Problem 66E ### 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

# Let F ( x ) = ∫ 1 x f ( t )   d t , where f is the function whose graph is shown. Where is F concave downward? To determine

The interval for the function F lies concave downward.

Explanation

Given information:

The interval function is F(x)=1xf(t)dt.

Here, F(x) is function of x and t is a derivative function.

Show the Theorem of fundamental calculus (part 1) as shown in below.

F(x)=axf(t)dtF(x)=f(x)

Draw the graph for f as shown in below;

Calculation:

The function F(x)=1xf(t)dt (1)

Apply the theorem of fundamentals of calculus (part 1) in Equation (1)

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Study Guide for Stewart's Multivariable Calculus, 8th 