Textbook ExpertVerified Tutor
11 Nov 2021
Given information
Note that given, 
is differentiable and 
.
Step-by-step explanation
Step 1.
You are correct if you only assume is differentiable on 
. If is discontinuous at the endpoints you could have a problem. The fact that is differentiable in the interior of the interval implies that it is continuous on the interior, but the endpoints could be troublesome.
is differentiable on . If is discontinuous at the endpoints you could have a problem. The fact that is differentiable in the interior of the interval implies that it is continuous on the interior, but the endpoints could be troublesome.Let 
and 
otherwise.
and otherwise.Therefore, 
for all 
.
for all .
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 2a
- Problem 2b
- Problem 3
- Problem 3a
- Problem 3b
- Problem 4
- Problem 5
- Problem 5b
- Problem 5c
- Problem 5d
- Problem 6
- Problem 6a
- Problem 6b
- Problem 6c
- Problem 7
- Problem 7b
- Problem 7d
- Problem 08
- Problem 8
- Problem 8a
- Problem 9
- Problem 9a
- Problem 9b
- Problem 9c
- Problem 9d
- Problem 10
- Problem 10a
- Problem 10b
- Problem 11
- Problem 11e
- Problem 12
- Problem 13
- Problem 13b
- Problem 14
- Problem 14b
- Problem 26