Find the constants and so that g(x)= cases Ax^ 2 +Bx+3, & x<1, 4x-5, & x 1 cases is…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Find the constants AA and BB so that g(x)={Ax2+Bx+3,x<1,4x−5,x≥1g(x)= \begin{cases} Ax^{2}+Bx+3, & x<1,\\ 4x-5, & x\ge 1 \end{cases} is both continuous and differentiable at x=1x=1.

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