Suppose f(x)= cases p(x), & x<3 q(x), & x 3

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Suppose f(x)={p(x),x<3q(x),x≥3.f(x)=\begin{cases}p(x), & x<3\\ q(x), & x\ge 3.\end{cases} The functions pp and qq are differentiable on their respective intervals. Which of the following statements, if true, guarantees that ff is differentiable at x=3x=3? (a) p′(3)=q′(3)p'(3)=q'(3) (b) p(3)=q(3)p(3)=q(3) and p′(3)=q′(3)p'(3)=q'(3) (c) p(3)=q(3)p(3)=q(3) (d) p(3)=q(3)p(3)=q(3) and p′(3)p'(3) and q′(3)q'(3) both exist

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