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Let g(x) = 1° 1 on I = [0, 1]. Verify that g satisfies the conditions of the Mean Value Theorem on I. Find all numbers c E (0, 1) that satisfy the conclusion of the Mean Value Theorem.

Let g(x) = 1° 1 on I = [0, 1]. Verify that g satisfies the conditions of the Mean Value Theorem on I. Find all numbers c E (0, 1) that satisfy the conclusion of the Mean Value Theorem.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
1 Let g(x) = on I = [0, 1]. 1+ x Verify that g satisfies the conditions of the Mean Value Theorem on I. Find all numbers c e (0, 1) that satisfy the conclusion of the Mean Value Theorem.
Transcribed Image Text:1 Let g(x) = on I = [0, 1]. 1+ x Verify that g satisfies the conditions of the Mean Value Theorem on I. Find all numbers c e (0, 1) that satisfy the conclusion of the Mean Value Theorem.
Expert Solution
Step 1

Given:

g(x)=11+x on I=[0,1]

Step 2

Explanation:

The mean value theorems states that for a continuous and a differentiable function

f(x) on the interval [a, b] there exists such number c from that interval,

such that

f'(c)=f(b)-f(a)b-a

Step 3

Continuous:

In the graph below in the interval [0, 1] the function is continuous.

Advanced Math homework question answer, step 3, image 1

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