Consider the piecewise function g(x)= cases cx^ 2 +d, & x<1 x, & x 1 cases Which…

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

Problem

Consider the piecewise function g(x)={cx2+d,x<1ln⁡x,x≥1g(x)=\begin{cases} cx^{2}+d, & x<1 \\ \ln x, & x\ge 1 \end{cases} Which ordered pair (c,d)(c,d) makes gg both continuous and differentiable at x=1x=1? (a) (1,−1)(1,-1) (b) (12,0)\left(\dfrac12,0\right) (c) (12,−12)\left(\dfrac12,-\dfrac12\right) (d) (0,0)(0,0)

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