Question

the height h (in feet) of a certain aircraft t seconds after it leaves the ground is modeled by h(t)=-9.1t^2+591.5t+20,288.125. What is the maximum height that the airplane reaches?

Answer 1

29900 feet

Explanation:

First, we calculate the derivative of the function h(t):

`(d)/(dh) = -18.2(t-32.5)\\\\`

After we have the derivative function - we insert 0 on the left side of the equation to find all possible function local maxima:

`0 = -18.2(t-32.5)\\t = 32.5`

From above equation we know the plane reached maximum height at time of 32.5 seconds, now we just insert the calculated value into the original function:

`-9.1* 32.5^2+591.5 * 32.5+20288.125 = 29900`

Voila! :D