### Home > CALC > Chapter 4 > Lesson 4.4.2 > Problem 4-142

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*