Consider the following piecewise defined function:

x + 5 if x < 3 f(x)= 4x+1 ifx3

(a) (6 points) Show that f(x) is continuous at x = 3.

(b) (14 points) Using the limit definition of the derivative, and com- puting the limits from both sides, show that f(x) is differentiable at x = 3.