Susan throws a softball upward into the air at a speed of 32 feet per second from a 24 dash foot platform. the distance upward that the ball travels is given by the function f left parenthesis t right parenthesis equals negative 16 t squared plus 32 t plus 24 . what is the maximum height of the? softball

In this problem, we don't need to come up with an equation anymore because it is already given. The speed and the length of the platform is already incorporated in the equation:

f(t) = 16t² +32t + 4

Now, we apply the concepts learned in Calculus. To find the maxima or minima of the function, you find the first derivative of the equation and equate it to zero. Using the formulas essential in differentiation, the derived form is

f'(t) = -32t + 32 = 0

Simplifying the equation:

-32(t-1) = 0
t - 1 = 0
t = 1

Since f(t) represents the distance, let's substitute t=-1 to the original equation to determine the maximum height:

f(-1) = -16(1)² +32(1) + 4 = 20 

That means that the maximum height is 20 feet.