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


1