Show that the function f(x) = |x|, x∈R, is continuous but not differentiable at x=3.

f(x)=|x|; x=3
LHD=f'(3-)=lim_{h→0}f(3-h)-f(3)/-h=lim_{h→0}|3-h|-|3|/-h=lim_{h→0}|-h|/-h=lim_{h→0}h/-h=-1
RHD=f'(3+)=lim_{h→0}f(3+h)-f(3)/h=lim_{h→0}|3+h|-|3|/h=lim_{h→0}=|h|/h=lim_{h→0}h/h=1
As LHD≠RHD
Therefore, f is not differentiable.
Again,
LHL=lim_{x→3-}|x|=lim_{h→0}|3-h|=lim_{h→0}|-h|=0
RHL=lim_{x→3+}|x|=lim_{h→0}|3+h|=lim_{h→0}|h|=0
Since LHL=RHL
Therefore, f is continuous at x=3.