Exercise 2: Consider the function: f (x) = 0. We have shown that f is not continuous at x = 0, and that x- f(x) is continuous at x = 0. (a) Show that x- f(x) is not differentiable at x = 0. (b) Show that the function x2 - f(x) is differentiable at x = 0. (c) [Challenge] Generalize (b): Prove that if f(x) is continuous at 0, then x-f(x) is differentiable at 0.
Exercise 2: Consider the function: f (x) = 0. We have shown that f is not continuous at x = 0, and that x- f(x) is continuous at x = 0. (a) Show that x- f(x) is not differentiable at x = 0. (b) Show that the function x2 - f(x) is differentiable at x = 0. (c) [Challenge] Generalize (b): Prove that if f(x) is continuous at 0, then x-f(x) is differentiable at 0.
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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ex2 hw4
![Exercise 2: Consider the function:
f (x)
= 0.
We have shown that f is not continuous at x = 0, and that x- f(x) is continuous at x = 0.
(a) Show that x- f(x) is not differentiable at x = 0.
(b) Show that the function x2 - f(x) is differentiable at x = 0.
(c) [Challenge] Generalize (b): Prove that if f(x) is continuous at 0, then x-f(x) is differentiable at 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff121ba60-7058-4a7c-893c-99f8ff2d6afa%2F1b2328f6-dcae-4f9d-859e-a43fcc5a0284%2Fj8c71zq.png&w=3840&q=75)
Transcribed Image Text:Exercise 2: Consider the function:
f (x)
= 0.
We have shown that f is not continuous at x = 0, and that x- f(x) is continuous at x = 0.
(a) Show that x- f(x) is not differentiable at x = 0.
(b) Show that the function x2 - f(x) is differentiable at x = 0.
(c) [Challenge] Generalize (b): Prove that if f(x) is continuous at 0, then x-f(x) is differentiable at 0.
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