When a baseball is thrown upward, its height is a function of time. If this function is given by formula h (t) = -16t^2+24t+5, what is the maximal height it reaches?

Nevermind I got it

Answer: the maximal height is 14.75 units of distance.

Step-by-step explanation:

We want to find the maximum height of the function

h (t) = - 16*t^2 + 24*t + 5

In order to find the maximum, we need to find the value of t where the derivate of h (t) is equal to zero, then we evaluate our original function in that time.

The derivate of h (t) (or the vertical velocity) is:

h' (t) = 2 * (-16) * t + 24 = - 32*t + 24

we want to find the value of such:

0 = - 32*t + 24

32*t = 24

t = 24/32 = 0.75

Now we evaluate our height function in that value.

h (0.75) = - 16*0.75^2 + 25*0.75 + 5 = 14.75 units