The correct option is D f(x) = maximum (x,-x)
Functions in options (a), (b) and (c) are ploynomail functions and hence differentiable
Let us verify option (d)
f(x) = maximum (x, -x)
f(x) = |x|={+x,x>0−x,x<0
so LD (Left derivative) = -1
& RD (Right derivative) = +1
∵LD≠RD
The function is not differentiable at x = 0