A pumpkin is launched directly upwards at 72 feet per second from a platform 12 feet high. The pumpkin's height, h, at time t seconds can be represented by the equation h (t) = - 16t^2+72t+12. Find the maximum height of the pumpkin and the time it takes to reach it.

93 feet

Step-by-step explanation:

Let us first find the time it takes to reach the maximum height. We can do this by differentiating the height function to get velocity:

dh (t) / dt = v (t) = - 32t + 72

The maximum height will occur when the velocity becomes 0. Therefore, the time it takes to reach maximum height is:

0 = - 32t + 72

32t = 72

t = 72/32 = 2.25 seconds

Therefore, the maximum height of the pumpkin is:

h (2.25) = - 16 (2.25) ^2 + 72 (2.25) + 12

h (2.25) = - 81 + 162 + 12

h = 93 feet