Consider the function f(x)= cases ax^ 2 +bx+2, & x<1 x+3 , & x 1 cases For which…

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

Problem

Consider the function f(x)={ax2+bx+2,x<1x+3,x≥1f(x)=\begin{cases} ax^{2}+bx+2, & x<1\\ \sqrt{x+3}, & x\ge 1 \end{cases} For which ordered pair (a,b)(a,b) is ff both continuous and differentiable at x=1x=1? (a) (12, −12)\left(\dfrac12,\,-\dfrac12\right) (b) (14, −14)\left(\dfrac14,\,-\dfrac14\right) (c) (−14, 14)\left(-\dfrac14,\,\dfrac14\right) (d) (0, 14)\left(0,\,\dfrac14\right)

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