determine whether the function f(x) = 1 - |x| is differentiable at x = 0 by considering lim h→0 ｛f (0+h) - f (0)｝/h. Created by Lok. science-mathematics-en - mathematics-en

determine whether the function f(x) = 1 - |x| is differentiable at x = 0 by considering lim h→0 (f (0+h)

May 2021 2 161 Report

determine whether the function f(x) = 1 - |x| is differentiable at x = 0 by considering lim h→0 (f (0+h) - f (?

determine whether the function f(x) = 1 - |x| is differentiable at x = 0 by considering lim h→0 ｛f (0+h) - f (0)｝/h

Suppose that h ≥ 0. Then:

[f(0+h) - f(0)]/h = [(1 - |h|) - 1]/h = -h/h = -1.

On the other hand, if h < 0,

[f(0+h) - f(0)]/h = [(1 - |h|) - 1]/h = h/h = 1.

The left-hand limit and the right-hand limit will never agree at 0.