BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 1RQ
To determine

Whether the statement, if f(c)=0 , then f has a local maximum or minimum at c is true or false.

Expert Solution

Answer to Problem 1RQ

The given statement is false.

Explanation of Solution

Reason:

If f(c)=0 then the tangent line of f will be parallel to the x-axis and it does not guarantee of the existence of local maximum or local minimum.

For example, consider the function f(x)=x3 .

Differentiate with respect to x.

f(x)=ddx(x3)=3x2

Set f(x)=0 to obtain,

3x2=0x=0

For all non-zero values of x, f(x) is increasing thus x=c is an inflection point but not local maximum or minimum.

Therefore, the given statement is false.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!