Chapter 3.3, Problem 96E

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

True or False? In Exercises 91-96, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The relative maxima of the function f are f ( 1 ) = 4 and f ( 3 ) = 10 , Therefore, f has at least one minimum for some x in the interval (1, 3).

To determine
Whether the provided statement,“A function with two maximas f(1)=4 and f(3)=10 would have a minima in the interval (1,3)” is true or false.

Explanation

Given:

The statement “A function with two maximas f(1)=4 and f(3)=10 would have a minima in the interval (1,3).

Explanation:

According to the first derivative test, for a critical point c of a function f(x),

If f'(x) changes sign from a negative value to a positive value at the point c, the f is said to have a relative minima at the point c.

If f'(x) changes sign from a positive value to a negative value at the point c, the f is said to have a relative maxima at the point c

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