question 1 (1 point) A rectangle has perimeter 12 meters. The largest its area can be is m2. (Enter a number for your answer. Do NOT enter the units.) Note that we want the area here (not the dimensions of the rectangle). D View hint for Question 1 Question 2 (1 point) . 4 The function f(a) = 4 3x3 - 1 is concave down on the interval(s) (select all that apply): This function is never concave down. O (0, 6) O ( - 00, 6 ) O (6, 00 ) O ( -00, 0 )Question 3 (1 point) 2 3 TRUE or FALSE: If f"(p) = 0, then p is an inflection point of f. O TRUE 6 FALSE 8 9 D View hint for Question 3 Question 4 (1 point) Let f(ac) = a3/5(x - 3). The inflection point(s) of f(a) is(are) (choose all that apply): O x =0 This function does not have any inflection points. O a = x = 3 c = -3 4point) The graphs A (blue), B (red), and C (green) are the graphs of a function f(x) and its derivatives, f' (x) and f"(x). Match the graph to the corresponding function. 110 1.0 B f (ac) 1. A (blue) f" (2) 2. B (red) f' (20 ) 3. C (green)Question 6 (1 point) 1 2 3 The following is a graph of the first derivative of the function f(x). On which of the following intervals is f(x) concave down? 4 U O 7 9 C B G -3 -2 -1D 1-1 E.2 Co F O ( F, G) O ( A, C) O ( D, E) O ( D, G ) O ( B, D )Question 7 (1 point) Let g(x) be a function such that g(a) > 0 for all x, and g' (2) = -g(2) for all x. A function f(x ) has derivative hof' ( 2 ) = (2 - 3) g(2 ) for all x. Which one of the following statements is FALSE? Of(x) is concave up on (4, 00) . Of" (20) = (4 - 20) g(20). Of(x) is decreasing on (-0o, 3). Of (ze) has an inflection point at x = 4. The absolute minimum of f(a) on (-oo, oo) occurs at x = 3. Question 8 (1 point)Question 8 (1 point) A cylindrical garden compost container with a circular base of diameter a and height y is to be made to contain 271 fts of soil. The container does not have a lid, that is, the container has an open top. What are the dimensions of the container that minimize the amount of material used to build the container ? Hint: The area of a circle of radius r is Tr2 . A cylinder (with bottom and top lid) with height h and radius r has volume Trzh, and has surface area 2rrh + 2mr. Ox = 6 ft and y = 3 ft. Ox = 2ft and y = 27 ft. Ox = 18 ft and y = 3 - ft . Ox = 2V3 ft and y = 9 ft. Ox = 3(2 ) 3 ft and y = 33/4ft. Question 9 (1 point)e 1: Question 9 (1 point) Jessica is in a kayak 3 km offshore from a straight road. She wishes to reach a hiking N 3 trail which is located 10 km down the road from the nearest point on the road to her. She can paddle at 4 km/h and can walk along the road at 5 km/h. How many kilometers should she walk in order to minimize her travel time? 5 6 Kayak Nearest point on road 8 9 Hiking trail Note: The above diagram is not drawn to scale. 6 km O (10 - V3) km O (10 - V5) km 10 km 0km