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# The Mean Value Theorema. Show that decreases on every

ISBN: 9780321884077 57

## Solution for problem 15PE Chapter 4

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 15PE

The Mean Value Theorem

a. Show that decreases on every interval in its domain.

b. How many solutions does the equation have? Give reasons for your answer.

Step-by-Step Solution:

Step 1 of 6:

a)In this problem, we need to show that  decreases on every interval in its domain.

Step 2 of 6:

Given function is:

Now differentiate on both sides with respect to t we get.

, since

Therefore, …….(1)

Step 3 of 6:

We know that, sin(x) lies between [-1,1].

So, .

Therefore, .

is always falling.

Therefore, decreases on every interval in its domain.

Step 4 of 6

Step 5 of 6

##### ISBN: 9780321884077

The answer to “The Mean Value Theorema. Show that decreases on every interval in its domain.b. How many solutions does the equation have? Give reasons for your answer.” is broken down into a number of easy to follow steps, and 25 words. This full solution covers the following key subjects: Answer, decreases, domain, equation, every. This expansive textbook survival guide covers 138 chapters, and 9198 solutions. The full step-by-step solution to problem: 15PE from chapter: 4 was answered by , our top Calculus solution expert on 08/01/17, 02:37PM. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. Since the solution to 15PE from 4 chapter was answered, more than 222 students have viewed the full step-by-step answer.

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