Explanation:
A batter hits a baseball into the air. The formula that models the baseball’s height above the ground, y, in feet, x seconds after it is hit is given by :
[tex]y=-16x^2+64x+5[/tex].........(1)
(a) We need to find the maximum height reached by the baseball. The maximum height reached is calculated by differentiating equation (1) wrt x as :
[tex]\dfrac{dy}{dx}=0[/tex]
[tex]\dfrac{d(-16x^2+64x+5)}{dx}=0[/tex]
[tex]-32x+64=0[/tex]
x = 2 seconds
(b) The height of the ball is given by equation (1) and putting the value of x in it as :
[tex]y=-16(2)^2+64(2)+5[/tex]
y = 69 feets
So, at 2 seconds the baseball reaches its maximum height and its maximum height is 69 feets.
