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4-126.

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.