# Continuous but Not Smooth

Calculus Level 2

Given that the following function is continuous and diﬀerentiable.

$f(x) = \begin{cases} ax + b & \quad x \geq 0 \\ \sin 2x & \quad x < 0 \end{cases}$

What is the value of $$a+b$$?

This problem is slightly changed from a practice problem from the MIT OpenCourseWare.

×