Show that ƒ(x) = |x-5| is continuous but not differentiable at x=5
Left hand limit at x = 5
Right hand limit at x = 5
Also f(5) = |5 – 5 |= 0
As,
= f(5)
Therefore, f(x) is continuous at x = 5
Now, lets see the differentiability of f(x)
LHD at x = 5
RHD at x = 5
Since, LHD ≠ RHD
Therefore,
f(x) is not differentiable at x = 5