Left hand limit at x = 5
\(\lim\limits_{x \to 5^-}\) |x-5| = \(\lim\limits_{x \to 5}\) (5-x) = 0
Right hand limit at x = 5
\(\lim\limits_{x \to 5^+}\) |x-5| = \(\lim\limits_{x \to 5}\) (x-5) = 0
Also f(5) = |5 – 5 |= 0
As,
\(\lim\limits_{x \to 5^-}\) f(x) = \(\lim\limits_{x \to 5^+}\) (5-x) = 0= f(5)
Therefore, f(x) is continuous at x = 5
Now, lets see the differentiability of f(x)
LHD at x = 5
Since, LHD ≠ RHD
Therefore,
f(x) is not differentiable at x = 5