Let h(x)= cases a x^ 3 +2x^ 2 -x+d,&x 1 m x^ 2 +5x+p,&x>1 cases Given that is…

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

Problem

Let h(x)={ax3+2x2−x+d,x≤1mx2+5x+p,x>1h(x)=\begin{cases}a x^{3}+2x^{2}-x+d,&x\le 1\\ m x^{2}+5x+p,&x>1\end{cases} Given that hh is continuous at x=1x=1, that h′h' and h′′h'' are also continuous at x=1x=1, and that h(0)=0h(0)=0, determine the values of a, d, m,a,\,d,\,m, and pp.

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