Answer:
36 feet
Step-by-step explanation:
Height of the baseball;
[tex]f(x) = - 0.1 {x}^{2} + 4x + 6[/tex]
At maximum height of the ball,
f'(x) =
[tex] \frac{dy}{dx} = 0[/tex]
[tex]( - 0.2 \times 2)x + 4 = 0[/tex]
-0.4x + 4 = 0
0.4x = 4 Divide both sides by 0.4
x = 10.
This means that the maximum height of the ball is when the horizontal distance x = 10 feet.
Maximum height = f(10) =
[tex]( - 0.1) {10}^{2} + 4(10) + 6[/tex]
= (-0.1 × 100) + 40 + 6
= -10 + 46
= 36 feet
Hence, the maximum height of the ball is 36 feet
