Answer to Question #65671 in Math for Droner

Question

The thickness of the ice on a lake for one week is modelled by the function:a) T(d)=-0.1d^3+1.2d^2-4.4d+14.8
where T is the thickness in cm and d is the number of days after December 31st. The graph of the function is provided below.

a) Determine the average rate of change in the thickness of the ice over 7 days.

b) When do you think the warmest day occurred during the week? Justify your answer.

c) Estimate the instantaneous rate of change at the point you chose in b).

d) Why is this called the estimated instantaneous rate of change?

e) Were your answers to the average rate of change the same as the estimated instantaneous rate of change? Explain why or why not.