Mathematics

Problem

Suppose

f(x)=\begin{cases}p(x), & x<3\\ q(x), & x\ge 3.\end{cases}

The functions

p

and

q

are differentiable on their respective intervals. Which of the following statements, if true, guarantees that

f

is differentiable at

x=3

? a)

p'(3)=q'(3)

p(3)=q(3)

and

p'(3)=q'(3)

p(3)=q(3)

p(3)=q(3)

and

p'(3)

and

q'(3)

both exist