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Determine the value of 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 'differentiability 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 4-152 HW eTool