Question

Prove that the greatest integer function defined by f (x)=[x],0 < x < 3 is not differentiable at x = 1 and x = 2.

Answer 1

It is known that a function f is differentiable at a point x = c in its domain if both

To check the differentiability of the given function at x = 1, consider the left hand limit of f at x = 1

Since the left and right hand limits of f at x = 1 are not equal, f is not differentiable at x = 1

To check the differentiability of the given function at x = 2, consider the left hand limit of f at x = 2

Since the left and right hand limits of f at x = 2 are not equal, f is not differentiable at x = 2