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

Question

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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

Students have asked these similar questions

Evaluate the next integral

1. For each of the following, find the critical numbers of f, the intervals on which f is increasing or decreasing, and the relative maximum and minimum values of f. (a) f(x) = x² - 2x²+3 (b) f(x) = (x+1)5-5x-2 (c) f(x) = x2 x-9 2. For each of the following, find the intervals on which f is concave upward or downward and the inflection points of f. (a) f(x) = x - 2x²+3 (b) g(x) = x³- x (c) f(x)=x-6x3 + x-8 3. Find the relative maximum and minimum values of the following functions by using the Second Derivative Test. (a) f(x)=1+3x² - 2x3 (b) g(x) = 2x3 + 3x² - 12x-4

Find the Soultion to the following dy differential equation using Fourier in transforms: = , хуо, ухо according to the terms: lim u(x,y) = 0 x18 lim 4x (x,y) = 0 x14 2 u (x, 0) = =\u(o,y) = -y لو

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.

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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.

Want to see more full solutions like this?

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

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.

Concept explainers

Videos

Answer to Problem 1RE

Explanation of Solution

Want to see more full solutions like this?

Chapter 14 Solutions

Additional Math Textbook Solutions