Let f: [a, b] → R be differentiable and that m≤ f'(x) ≤M for all x € [a, b]. (b) Let x € [a, b]. Show that f(a) +m(x-a) ≤ f(x) ≤ f(a) + M(x -a). (c) Suppose that g: [0,5] → R be differentiable, g(0) = 0, and that that -3 ≤ g'(x) ≤ 3, use part (b), to show that -5x ≤ g(x) ≤ 5z.
Let f: [a, b] → R be differentiable and that m≤ f'(x) ≤M for all x € [a, b]. (b) Let x € [a, b]. Show that f(a) +m(x-a) ≤ f(x) ≤ f(a) + M(x -a). (c) Suppose that g: [0,5] → R be differentiable, g(0) = 0, and that that -3 ≤ g'(x) ≤ 3, use part (b), to show that -5x ≤ g(x) ≤ 5z.
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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Hint: part c is false, show that its not true
![Let f: [a, b] → R be differentiable and that m≤ f'(x) ≤M for all x € [a, b].
(b) Let x € [a, b]. Show that
f(a) +m(x-a) ≤ f(x) ≤ f(a) + M(x -a).
(c) Suppose that g: [0,5] → R be differentiable, g(0) = 0, and that that -3 ≤ g'(x) ≤ 3,
use part (b), to show that
-5x ≤ g(x) ≤ 5z.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fecc418e3-a973-4d51-90e0-10d2ad078b59%2Ff06ed55f-f62c-4aab-8cb1-343eaa1c9985%2Fs6nsgb5_processed.png&w=3840&q=75)
Transcribed Image Text:Let f: [a, b] → R be differentiable and that m≤ f'(x) ≤M for all x € [a, b].
(b) Let x € [a, b]. Show that
f(a) +m(x-a) ≤ f(x) ≤ f(a) + M(x -a).
(c) Suppose that g: [0,5] → R be differentiable, g(0) = 0, and that that -3 ≤ g'(x) ≤ 3,
use part (b), to show that
-5x ≤ g(x) ≤ 5z.
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