4. Indicate whether each statement is true or false by circle T for true or F for false. (No justification or explanation required.) [1] (a) Every continuous function on [a, b] has a local maximum. T F [1] (b) If f"(c) = 0, then (c, f(c)) is an inflection point . T F [1] (c) If f (x ) = 72, then 0 is a critical point. [1] (d) If y = e2, then y' = 2e T F [1] (e) If f"(c) 0 on (-2, 1), and (6, 9). . f"(x) 0 on (-oo, 0), and (12, 00). For full marks clearly and carefully label all intercepts, relative extrema, inflection points and asymptotes. 4 3 2 1 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 -1 -2 -3 -46. A box with a square base and open top must have a volume of 442 368 cm3 . We wish to nd the dimensions of the box that minimize the amount of material used. [ 8 points] Follow the following steps: First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible. 1.A(x) = Next, find the derivative, A'(x) . 2.A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0 . [Hint: multiply both sides by x2 .] 3.A'(x) = 0 whenx = We next have to make sure that this value ofx gives a minimum value for the surface area. Let's use the second derivative test. Find A " (x) . 4. A"(x) 2 Evaluate A " (x) at the 3: -value you gave above