(a) According to the model f, what is the average rate of change of the amount of dirt removed over the time interval 6 ? 1 ? 12 hours?(b) Use the data in the table to approximate f' (9), the instantancous rate of change in the amount of dint removed. in cubic meters per hour, at time t = 9hours. Show the computations that lead to your answer.(c) Is f continuous for O ? t ? 12? Justify your answer.(d) Find f' (2), the instantaneous rate of change in the amount of dirt removed, in cubic meters per hour, at time t= 2 hours.

uestion 7 CALCULATOR IS ALLOWED FOR THIS QUESTION. ow all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give athematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and mpleteness of your methods as well as your answers. Answers without supporting work will usually not receive credit. less otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. less otherwise specified, the domain of a function f is assumed to be the set of all real numbers I for which f () is a real number. f (t ) = 48t + t2- for 0