Question

The flight of a fireworks rocket is given by the function: h(t)= -16t^2 + 84t+5 Where h(t) is the height in feet and t, the time in seconds. How long will the rocket take to reach its maximum height?Round your answer to 2 decimal places.

Answer 1

Given:

The flight of a fireworks rocket is given by the function:

`h(t)=-16t^2+84t+5`

Required:

How long will the rocket take to reach its maximum height?

Step-by-step explanation:

We will first find critical points

`\begin{gathered} h^(\prime)(t)=-32t+84 \\ \text{ Now, put }h^(\prime)(t)=0 \\ t=(21)/(8) \\ \text{ At }t=(21)/(8)\text{ we get stationary points.} \end{gathered}`

To check maximum and minimum value

`\begin{gathered} h^(\prime)^(\prime)(t)=-32(<0) \\ \text{ At }t=(21)/(8)\text{ the function is maximum.} \end{gathered}`

Asnwer