Mathematics

Problem

Let

h(x)=\begin{cases}a x^{3}+2x^{2}-x+d,&x\le 1\\ m x^{2}+5x+p,&x>1\end{cases}

Given that

h

is continuous at

x=1

, that

h'

and

h''

are also continuous at

x=1

, and that

h(0)=0

, determine the values of

a,\,d,\,m,

and

p