Answer:
<em>The ball reaches its maximum height at 2.5 seconds</em>
<em>The maximum height is 100 feet</em>
Step-by-step explanation:
<u>Maximum Value of Functions</u>
We use the derivative of a function to find its maximum or minimum value over a given interval.
Given a function y=f(x), the first derivative criterion establishes if x=a is such that:
f'(a)=0, and f''(a) < 0 then x=a is a maximum of f.
The height h in feet of a ball after t seconds is:
Find the first derivative:
Equate to 0:
Subtract 80:
Divide by -32:
t=2.5 seconds
Find the second derivative:
h''(t)=-32
Since h''(t) is always negative, then
The ball reaches its maximum height at 2.5 seconds
To find the value of the maximum height, substitute t=2.5 into the function:
The maximum height is 100 feet