Answer:
The rocket reaches its maximum height at 2.25 seconds.
It’s maximum height is 88 feet.
This can be found by finding the derivative of the function and setting it to zero.
-16x² +72x + 7
Taking first derivative and setting to zero:
-32x + 72 = 0
x = -72/-32=2.25
Find the height when x is 2 seconds by substituting this value into the original function:
-16 * (2.25)² + 72 * 2.25 + 7 = 88
Therefore the maximum turning point of the parabola will be (2.25, 88)