Final answer:
To find the maximum and minimum of the function h(t) = -16t² + 160t, we need to determine the critical points. The critical points occur when the derivative of the function is equal to zero. We can find the derivative of h(t) and set it equal to zero to solve for t. After finding the values of t, we substitute them back into the function to find the corresponding maximum and minimum values of h(t).
Step-by-step explanation:
To find the maximum and minimum of the function h(t) = -16t² + 160t, we need to determine the critical points. The critical points occur when the derivative of the function is equal to zero. We can find the derivative of h(t) and set it equal to zero to solve for t. After finding the values of t, we substitute them back into the function to find the corresponding maximum and minimum values of h(t).
First, let's find the derivative of h(t) by applying the power rule:
h'(t) = -32t + 160
Next, set the derivative equal to zero and solve for t:
-32t + 160 = 0
t = 5
Now substitute the value of t back into the original function to find the maximum and minimum values of h(t):
h(5) = -16(5)² + 160(5) = 800
Therefore, the maximum value of the function h(t) is 800, and there is no minimum value as the function does not have a downward-facing parabola.