Question

H = -5t2 + 30t + 10
a) What is the Rocket's maximum height?

Answer 1

The maximum height is 55

Explanation:

Step 1: Find the derivative with respect to t

`-5t^2 + 30t + 10`

`-5*2t + 30`

`-10t+30`

Step 2: Solve for t

`-10t + 30 - 30 = 0 - 30`

`-10t / -10 = -30 / -10`

`t = 3`

Step 3: Plug in 3 for t in the original equation

`h = -5(3)^2 + 30(3) + 10`

`h = -5(9) + 90 + 10`

`h = -45+90+10`

`h = 45 + 10`

`h = 55`

Answer: The maximum height is 55