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

4-142.

Find

*a*such that*f*(*x*) is differentiable at*x*= 1. Homework Help ✎

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