Statement :

If the function has derivative from left and right side at a point, then it is differentiable at that point.

Conisder a example .

The derivative of the function is .

Here the function has left hand derivative and the right hand derivative at .

Left hand derivative is .

Right hand derivative is .

The left hand derivative and the right hand derivative are not equal, hence it is not differentiable at .

Hence the function is continuous at any point but not differentiable at .

The statement is false.

The statement is false.