Let ƒ(x) = {(2+x),if x ≥0; (2-x), if x<0 Show that ƒ(x) is not derivable at x=0.

Question

Let  \(f(x) = \begin{cases} (2+x), & \quad \text{if } x≥0; \text{}\\ (2-x), & \quad \text{if } x<0 \text{} \end{cases}\)   Show that ƒ(x) is not derivable at x=0

Answer 1

Given function   \(f(x) = \begin{cases} (2+x), & \quad \text{if } x≥0; \text{}\\ (2-x), & \quad \text{if } x<0 \text{} \end{cases}\) 

HD at x = 0:

As, LHD ≠ RHD 

Therefore, 

f(x) is not differentiable at x = 0