Given:
The flight of a fireworks rocket is given by the function:
[tex]h(t)=-16t^2+84t+5[/tex]Required:
How long will the rocket take to reach its maximum height?
Explanation:
We will first find critical points
[tex]\begin{gathered} h^{\prime}(t)=-32t+84 \\ \text{ Now, put }h^{\prime}(t)=0 \\ t=\frac{21}{8} \\ \text{ At }t=\frac{21}{8}\text{ we get stationary points.} \end{gathered}[/tex]To check maximum and minimum value
[tex]\begin{gathered} h^{\prime}^{\prime}(t)=-32(<0) \\ \text{ At }t=\frac{21}{8}\text{ the function is maximum.} \end{gathered}[/tex]Asnwer
