The absolute maximum of a function always occurs where the derivative has a critical number.

Question

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Answer 1

Textbook Question

Chapter 14, Problem 1RE

The absolute maximum of a function always occurs where the derivative has a critical number.

Expert Solution & Answer

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

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Find the critical values of f then use the second derivative to determine if f has a relative maximum or relative minimum at each critical value.

Answer 2

Textbook Question

Chapter 14, Problem 1RE

The absolute maximum of a function always occurs where the derivative has a critical number.

Expert Solution & Answer

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 14, Problem 1RE

The absolute maximum of a function always occurs where the derivative has a critical number.

Expert Solution & Answer

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 14, Problem 1RE

The absolute maximum of a function always occurs where the derivative has a critical number.

Expert Solution & Answer

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

Answer 8

Expert Solution & Answer

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer to Problem 1RE

The statement is False.

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Whether the statement “The absolute maximum of a function always occurs where the derivative has a critical number” is true or false.

Answer 12

Answer to Problem 1RE

The statement is False.

Answer 13

Explanation of Solution

Let f(x) be a continuous function on the closed interval then the absolute extrema of f(x) might occur at the end point of the interval.

It may be occur in critical points but not sure.

Therefore, the statement is False.

Answer 14

Ch. 14.1 - Find the absolute extrema of the function f(x) =...Ch. 14.1 - Find the locations and values of the absolute...Ch. 14.1 - Prob. 1WE Ch. 14.1 - Find all critical numbers for each of the...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Find the locations of any absolute extrema for the...Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E

The absolute maximum of a function always occurs where the derivative has a critical number.

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