CPM Homework Banner
4-142.

Find such that is differentiable at

In order to prove that is differentiable at , 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 , then it CANNOT be differentiable (even if the derivatives agree). So use the Three Conditions of Continuity to demonstrate that is continuous at .

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