1. (28) Sketch the graph of f(x) = (x -1)(x -2)3(x - 3) and find the following if they exist (if it does not exist, write DNE) . Give approximate values of a for the following: a. relative maximum point (s) a . C~ b. relative minimum point (s) b. *~ c. inflection point (s) C. XN d. interval (s) where f is concave down d. You may use the following: f'(2) = V(x -2)2(40x2 - 163x + 141) 15 6 (x - 3)3 (x - 1)2 Show your sign graph here 40 (x - 2)2(2 - 1.2) (2 - 2.8) ~ and 15\\ (x - 3)3 (x - 1)2 f"(2) =. 2(500x - 4075x3 + 11717x2 - 13893x + 5643) 225 (x - 3)8 Vx - 25(x-1)7 40(x - 0.9) (x - 1.6)(x - 2.5) (x - 3.1) ~ Show your sign graph here 9V (x -3)8 Vx - 25(x -1)72. (12) A bird, released from an island that is 5 km from the nearest point A on a straight shoreline, flies to a point B on the shoreline, and then flies along the shoreline (over land) to a point C 13 km from point A (point B is between A and C). If it takes 1.4 times as much energy to fly over water as it does over land, to what point B should the bird fly in order to minimize the total energy consumption in flying from the island to point C? Give exact answer simplified