Question

a ball is thrown into the air and its position is given by

\\h(t) = -4.3t^2 + 48t + 17,\\

where \\(h\\) is the height of the ball in meters \\(t\\) seconds after it has been thrown.

i. after how many seconds does the ball reach its maximum height? round to the nearest second.

ii. what is the maximum height? round to one decimal place.

Explanation:

Find the derivative of the height function

$$ h'(t) = -8.6t + 48 $$

Solve for the critical point where velocity is zero

$$
LATEXBLOCK0
$$

Calculate the maximum height at the critical point

$$
LATEXBLOCK1
$$

Answer:

Question I

After how many seconds does the ball reach its maximum height? Round to the nearest second.
<blank>6</blank> seconds

Question II

What is the maximum height? Round to one decimal place.
<blank>150.9</blank> meters