Consider the function h(x)= cases m x^ 2 , & x<1

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

Problem

Consider the function h(x)={mx2,x<1,ex−1+1,x≥1.h(x)=\begin{cases} m x^{2}, & x<1,\\ e^{x-1}+1, & x\ge 1. \end{cases} Find the value of mm such that hh is both continuous and differentiable at x=1x=1.

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