Answer:
The maximum height is 55
Step-by-step explanation:
Step 1: Find the derivative with respect to t
[tex]-5t^2 + 30t + 10[/tex]
[tex]-5*2t + 30[/tex]
[tex]-10t+30[/tex]
Step 2: Solve for t
[tex]-10t + 30 - 30 = 0 - 30[/tex]
[tex]-10t / -10 = -30 / -10[/tex]
[tex]t = 3[/tex]
Step 3: Plug in 3 for t in the original equation
[tex]h = -5(3)^2 + 30(3) + 10[/tex]
[tex]h = -5(9) + 90 + 10[/tex]
[tex]h = -45+90+10[/tex]
[tex]h = 45 + 10[/tex]
[tex]h = 55[/tex]
Answer: The maximum height is 55
