Answer:
16 meters
Step-by-step explanation:
The height function is given by:
[tex]h(x)=-(x+1)(x-7)\\h(x)=-(x^2+x-7x-7)\\h(x)=-x^2+6x+7[/tex]
The value of x, in seconds, for which the derivate of the height function is zero, is the time at which the maximum height occurs:
[tex]\frac{dh(x)}{dx}= h'(x)=-2x+6=0\\x=3[/tex]
For x = 3 seconds, the height is:
[tex]h(3)=-(3^2)+6*3+7\\h(3)=16\ m[/tex]
The maximum height that the ball will reach is 16 meters.
