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...

ex2 hw4

Extracted 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.