Which of the functions in Exercises 9–14 satisfy the hypotheses of the Mean Value Theorem on the given interval, and which do not? Give reasons for your answers. 9. f(x) = x²/3, [-1,8] 10. f(x) = x4/5, [0,1] 11. f(x) 3D Vx(1 — х), sin x -T

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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Which of the functions in Exercises 9–14 satisfy the hypotheses of the
Mean Value Theorem on the given interval, and which do not? Give
reasons for your answers.
9. f(x) = x²/3, [-1,8]
10. f(x) = x4/5, [0,1]
11. f(x) 3D Vx(1 — х),
sin x
-T<x < 0
х
12. f(x) =
0,
x = 0
Sx² – x,
{2x²
-2 < x<-1
13. f(x) =
2r?
— Зх — 3, —1 <x<0
[2r – 3,
(6x – x² – 7, 2<x< 3
0 < x< 2
14. f(x) =
Transcribed Image Text:Which of the functions in Exercises 9–14 satisfy the hypotheses of the Mean Value Theorem on the given interval, and which do not? Give reasons for your answers. 9. f(x) = x²/3, [-1,8] 10. f(x) = x4/5, [0,1] 11. f(x) 3D Vx(1 — х), sin x -T<x < 0 х 12. f(x) = 0, x = 0 Sx² – x, {2x² -2 < x<-1 13. f(x) = 2r? — Зх — 3, —1 <x<0 [2r – 3, (6x – x² – 7, 2<x< 3 0 < x< 2 14. f(x) =
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