The number of gallons of olive oil in a tank at time t is given by the twice-differentiable function A, where t is
measured in hours and 0 ≤ t ≤ 35. Values of A(t) at selected times t are given in the table above.
(a) Use the data in the table to estimate the rate at which the number of gallons of olive oil in the tank is changing
at time t= 10 hours. Show the computations that lead to your answer. Indicate units of measure.
(b) For 0 ≤ t ≤ 30, is there a time t at which A'(t) = 1/5? Justify your answer.

(c) The number of gallons of olive oil in the tank at time t is also modeled by the function G defined by
=
G(t) = 5t-2/3(t + 9)^3/2+ 28, where t is measured in hours and 0 ≤ t ≤ 35. Based on the model, at what
time t, for 0 ≤ t ≤ 35, is the number of gallons of olive oil in the tank an absolute maximum? Justify your
answer.
(d) For the function G defined in part (c), the locally linear approximation near t = 7 is used to approximate
G(8). Is this approximation an overestimate or an underestimate for the value of G(8) ? Give a reason for your answer.