The function is piecewise linear on with the following properties: • On

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

Problem

The function gg is piecewise linear on 0≤x≤80\le x\le 8 with the following properties: • On 0≤x≤30\le x\le 3, the slope of gg is 22. • On 3<x≤53< x\le 5, the slope of gg is −1-1. • On 5<x≤85< x\le 8, the slope of gg is 44. Let f(x)=g′(x)f(x)=g'(x). At which of the following xx–values does ff attain its minimum on the interval 0<x<80<x<8? (a) x=3x=3 (b) x=4x=4 (c) x=5x=5 (d) x=2x=2

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