In order to prove that f(x) is differentiable at x = 1, you must demonstrate that the derivatives agree from the left and right.
But do not forget that 'differentiablity implies continuity'. In other words, if the function is not continuous at x = 1, then it CANNOT be differentiable (even if the derivatives agree). So use the Three Conditions of Continuity to demonstrate that f(x) is continuous at x = 1.
Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 4-142 HW eTool