1. Oil flows into a tank according to the rate , and at the same time empties out at the rate , with both F(t) and E(t) measured in gallons per minute. How much oil, to the nearest gallon, is in the tank at time t = 12 minutes. You must show your setup but can use your calculator for all evaluations.
2. The figure below shows the graph of f ', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.
Find the x-value where f attains its absolute maximum value on the closed interval from x = -2 to x = 6. Justify your answer