A function satisfies and where f(x)= cases 2x+1, & x<2

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

Problem

A function FF satisfies F(0)=0F(0)=0 and F′(x)=f(x)F'(x)=f(x) where f(x)={2x+1,x<2,k,x≥2.f(x)= \begin{cases} 2x+1, & x<2,\\ k, & x\ge 2. \end{cases} For which value of kk is FF differentiable at x=2x=2? (a) 6 (b) 5 (c) 3 (d) 4

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