Answer:
36 feet
Step-by-step explanation:
Height of the baseball;
\(f(x) = - 0.1 {x}^{2} + 4x + 6\)
At maximum height of the ball,
f'(x) =
\(\frac{dy}{dx} = 0\)
\(( - 0.2 \times 2)x + 4 = 0\)
-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) =
\(( - 0.1) {10}^{2} + 4(10) + 6\)
= (-0.1 × 100) + 40 + 6
= -10 + 46
= 36 feet
Hence, the maximum height of the ball is 36 feet
