Question

The height of a soccer ball that is kicked from the ground canbe approximated by the function:y = -18x2 + 36xwhere y is the height of the soccer ball in feet x seconds after it is kicked.What is the soccer ball's maximum height in feet?

Answer 1

For this problem you have to derive the equation given:

`\begin{gathered} y^(\prime)=(-18x^2+36x)^(\prime)\text{ = -36x+}36 \\ \text{Now we equal to zero} \\ -36x+36=0 \\ \text{and we solve for x} \\ x=1 \end{gathered}`

If we derive y again we notice that y''=-36 that means that a maximum is reached for x=1, then the maximum height of the ball is

`y=-18(1^2)+36(1)=18`

y= 18 feet