Science:Math Exam Resources/Courses/MATH110/December 2014/Question 03 (e)/Statement

Now consider the function

$$g(x)={\begin{cases}e^{x}&{\text{if }}x\leq 0\\{\sqrt {x}}&{\text{if }}0<x<4\\\displaystyle mx+b&{\text{if }}x\geq 4.\end{cases}}$$

where ${\textstyle m}$ and ${\textstyle b}$ are constants. Find values for ${\textstyle m}$ and ${\textstyle b}$ such that ${\textstyle g(x)}$ is differentiable at ${\textstyle x=4.}$