1) Where is the function f(x) = - 5 Diff (2x - 4)3 increasing? A) at x = 30 B) for all x C) for x > 2 D) none of these 2) Find the x coordinates of all relative extreme points of f(x) = _x4 - 2x3 - 6x2 - 100 Solv ind the relative extrema of the function, if they exist. 3) f(x) = 2x2 + 8x + 9 Find the points of inflection. 4) f(x) = x3 - 3x2 + 2x + 15 solve the problem. 5) Suppose c(x) = x3 - 22x2 + 20,000x is the Com cost of manufacturing x items. Find a production level that will minimize the average cost of making x items. 6) A manufacturer estimates that the profit from producing x units of a commodity is -x2 + 40x - 100 dollars per week. What is the maximum profit he can realize in one week? Diff 7) Suppose a ball is thrown into the air and after t seconds has a height of h(t) = -16t2 + 80t feet. When will it reach its maximum height? solve the problem. 8) Suppose c(x) = x3 - 16x2 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items. Sol 9) What is the maximum area that can be enclosed in a rectangular shape with 100 feet of fence if one of the two long sides is not fenced (there is a natural boundary there)? solve the problem. 10) Find the number of units, x, that produces the maximum profit P, if C(x) = 10 + 28x and P = 100 - 2x