Question

In the summer the activity level of a certain type of lizard varies according to the time of day. A biologist has determined that the activity level is given by the function below, where t is the number of hours after 12 noon. When is the activity level highest? When is it lowest? a(t) = 0.008t^3 -0.287t^2 + 2.307t +^2 Choose the correct answer below. A. The highest level of activity occurs at 4:07 P.M., and the lowest level of activity occurs at 5:48 A.M. B. The highest level of activity occurs at 4:07 P.M., and the lowest level of activity occurs at 6:48 A.M. C. The highest level of activity occurs at 5:07 P.M., and the lowest level of activity occurs at 6:48 A.M. D. The highest level of activity occurs at 5:07 P.M., and the lowest level of activity occurs at 5:48 A.M.

Answer 1

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.