009A Sample Final 1, Problem 2

Consider the following piecewise defined function:

$f(x)=\left\{{\begin{array}{lr}x+5&{\text{if }}x<3\\4{\sqrt {x+1}}&{\text{if }}x\geq 3\end{array}}\right.$

(a) Show that  $f(x)$  is continuous at  $x=3.$

(b) Using the limit definition of the derivative, and computing the limits from both sides, show that  $f(x)$  is differentiable at  $x=3$.

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