Maximum height of the football

Question

The height of a football after it has been kicked can be modeled by the function . In the function, t is the time in seconds after the ball has been kicked and h(t) is the height of the ball in feet above the ground. Which is the maximum height of the football?

Answer 1

To solve, given the equation for the height of the football as a function of time t seconds, first take the derivative of h(t). To find a local maximum set this derivative equal to zero and solve for t. Now that you have the time of the local maximum height, plug t into the original equation h(t) and this will give you the maximum height of the football.