Show that function ƒ(x) = is continuous but not differentiable at x=1

Question

Philoid · Accepted Answer

Given function f(x) =

Left hand limit at x = 1:

Right hand limit at x = 1:

Also, f(1) = 1² – 1 = 0

As,

Therefore,

f(x) is continuous at x = 1

Now, let’s see the differentiability of f(x):

LHD at x = 2:

RHD at x = 2:

= 2 + 2 = 4

As, LHD ≠ RHD

Therefore,

f(x) is not differentiable at x = 2