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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 19E

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