Answer:
Therefore, the maximum value of the function occurs at t = 5.07, and the minimum value of the function occurs at t = -0.48.
Since 5.07 hours after 12 noon is 5:07 P.M., and -0.48 hours after 12 noon is 5:48 A.M., the highest level of activity occurs at 5:07 P.M., and the lowest level of activity occurs at 5:48 A.M.
Explanation:
The correct answer is C. The highest level of activity occurs at 5:07 P.M., and the lowest level of activity occurs at 6:48 A.M.
To find the highest and lowest values of the function, we can find its maximum and minimum values. The maximum value of a function is the highest value that the function takes on, and the minimum value is the lowest value that the function takes on.
To find the maximum and minimum values of a function, we can use the critical points of the function. A critical point of a function is a point in the domain of the function where the derivative of the function is equal to zero.
The derivative of the function a(t) is:
a'(t) = 0.024t^2 - 0.574t + 2.307
Setting a'(t) equal to zero and solving for t, we get the critical points:
t = 5.07
t = -0.48
The critical point at t = 5.07 is a maximum point, and the critical point at t = -0.48 is a minimum point.