Question

A Pumpkin gets launched into the air from a cliff above a pond. The following equation represents the height of the pumpkin from the pond, h(t)=−16t2+56t+32where t is time in seconds.  What is the maximum height the pumpkin reaches?

Answer 1

$h(t)=-16t^2+56t+32$

$h'(t)=-32t+56=0$

$t=56/32=1.75$

$h''(t)=-32<0$

So it is maximum

$h(t)=-16(1.75^2)+56(1.75)+32=81$