The graph of a function consists of three straight-line segments joining the points to

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

Problem

The graph of a function ff consists of three straight-line segments joining the points (−6,0)(-6,0) to (−2,4)(-2,4), then (−2,4)(-2,4) to (1,1)(1,1), and finally (1,1)(1,1) to (5,5).(5,5). Which of the following piecewise functions could represent f′f'? (a) f′(x)={4,−6<x<−2,−3,−2<x<1,4,1<x<5.f'(x)=\begin{cases}4,&-6<x<-2,\\-3,&-2<x<1,\\4,&1<x<5.\end{cases} (b) f′(x)={1,−6<x<−2,0,−2<x<1,1,1<x<5.f'(x)=\begin{cases}1,&-6<x<-2,\\0,&-2<x<1,\\1,&1<x<5.\end{cases} (c) f′(x)={1,−6<x<−2,−1,−2<x<1,1,1<x<5.f'(x)=\begin{cases}1,&-6<x<-2,\\-1,&-2<x<1,\\1,&1<x<5.\end{cases} (d) f′(x)={−1,−6<x<−2,1,−2<x<1,−1,1<x<5.f'(x)=\begin{cases}-1,&-6<x<-2,\\1,&-2<x<1,\\-1,&1<x<5.\end{cases}

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