### Home > CALC > Chapter 4 > Lesson 4.4.1 > Problem 4-126

4-126.

Sketch *g*(*x*) below and determine if it is differentiable at *x *= 2. Homework Help ✎

Differentiability implies continuity. If you are checking for differentiability, you also need to check for continuity.

To check for continuity:

*g*(2) = 2(sin(2 − 2)) + 1 =1

*g*(*x*) is continuous at *x* = 2.

To check for differentiability:

*g*'(2) = 2cos(2 - 2) = 2 ............................

Since both *g*(*x*) and *g*'(*x*) are continuous at *x* = 2, *g*(*x*) is differentiable at *x* = 2.