Determine the value of such that the function f(x)= cases kx+1, & x<2

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

Problem

Determine the value of kk such that the function f(x)={kx+1,x<2,x2−3,x≥2f(x)= \begin{cases} kx+1, & x<2,\\ x^{2}-3, & x\ge 2 \end{cases} is differentiable at x=2x=2.

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