Consider the piecewise function f(x)= cases x^ 2 -4x+3, & x<1

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

Problem

Consider the piecewise function f(x)={x2−4x+3,x<1,ax+b,x≥1.f(x)=\begin{cases} x^{2}-4x+3, & x<1,\\ ax+b, & x\ge 1. \end{cases} Which pair (a,b)(a,b) ensures that ff is differentiable at x=1x=1? (a) a=−2,  b=−2a=-2,\; b=-2 (b) a=2,  b=−2a=2,\; b=-2 (c) a=−2,  b=2a=-2,\; b=2 (d) a=−1,  b=1a=-1,\; b=1

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