Apumpkin is launched directly upwards at 72 feet per second from a platform 24 feet high. the pumpkins height, h, at time t seconds can be represented by the equation h(t) = -16t^2+ 72t +24.find the maximum height of the pumpkin and the time it takes to reach this point.

Maximum height =  105 feet

And, It takes 9/4 seconds to reach that point.

Step-by-step explanation:

Here the given function that shows the height of the pumpkin,

--------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,    

Again differentiating above equation with respect to t,

We get,  

For maximum or minimum,    

At t = 9/4 , h''(t) = Negative value,

Therefore, At t = 9/4 seconds, h(t) is maximum,

And, the maximum value is,

Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds

Maximum height =  105 feet

And, It takes 9/4 seconds to reach that point.

Step-by-step explanation:

Here the given function that shows the height of the pumpkin,

--------(1)

Where t is the time in second.

Differentiating equation (1) with respect to t,

We get,    

Again differentiating above equation with respect to t,

We get,  

For maximum or minimum,    

At t = 9/4 , h''(t) = Negative value,

Therefore, At t = 9/4 seconds, h(t) is maximum,

And, the maximum value is,

Therefore, the maximum height of the pumpkin is 105 feet at 9/4 seconds