Solution
Step 1:
Write the equation:
[tex]h\text{ = -16t}^2\text{ + 144t}[/tex]
Step 2
[tex]At\text{ maximum height, }\frac{dh}{dt}\text{ = 0}[/tex]
Step 3:
[tex]\begin{gathered} h\text{ = -16t}^2\text{ + 144t} \\ \\ \frac{dh}{dt}\text{ = -32t + 144} \\ \\ 32t\text{ = 144} \\ t\text{ = }\frac{144}{32} \\ t\text{ = 4.5} \end{gathered}[/tex]
Step 4
Substitute t = 4.5 into the height equation.
[tex]\begin{gathered} h\text{ = -16 }\times\text{ 4.5}^2\text{ + 144 }\times\text{ 4.5} \\ h\text{ = -324 + 648} \\ \text{h = 324} \end{gathered}[/tex]
