3 5 6 . . . 4 . . . 200 . All boxes With a square base and a volume of 50 it3 have a surface area given by 5(37.) : 2:172 + , :r where .7: is the length of the sides of the base. Find the absolute minimum oi the surface area function on the interval (0. oo). \Vl1at are the dimensions of the box with minimum surface area? Justify your answer. a. Find the critical points of the following function on the given interval. b. Find the absolute extreme values on the given interval, if they exist. g(:1:) = (:r 3)%(.T + 2) on [4. 4] . Find the intervals on which j is increasing and the intervals on which it is decreasing. 1T3?) = $2 7 21113: :10'2 . Let f(.:rr) = $2 7 1 on [74. 4]. (a) Locate the critical points of f. (b) Use the First Derivative Test to locate the local maximum and minimum values. (c) Identify the absolute maximum and minimum values of the function on the given interval (when they exist). . Determine the intervals on which the following function is concave up or concave down. Identify any inection points. j(.r) :1r4c"; + 3: . Let f(.:rr) = (.1? 7 c.)8 with c. is a constant. (a) Locate the critical points of f. (b) Use the First Derivative Test to locate the local maximum and minimum values (if possible). (c) Use the Second Derivative Test to locate the local maximum and minimum values (if possible)