Graph the function by finding the relative extrema and inflection points. You may also use intercepts to help. 6) f(x) =2x3 + 12x2 +18x 2 Solve the following optimization problems using Calculus techniques. 7) Of all numbers whose sum is 180, find the two that have the maximum product. That is, maximize Q = xy, where x + y = 180. 8) 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)?9) The cost of a computer system increases with increased processor speeds. The cost C of a system as a function of processor speed is estimated as C = 5S2 - 25 + 1800, where S is the processor speed in MHz. Find the processor speed for which cost is at a minimum. Round to the nearest tenth if necessary.Skills Check 5 MT 175 Name Please show all work for full credit, Circle or otherwise clearly indicate your answer to each question. Simplify all answers. Do not leave any negative exponents or complex fractions in your final answers. 1) Fill in all points that fit the following descriptions. You may have more than one point for some or all answers relative maximum_ relative minimun_ inflection point f(x) is increasing at f(x) is decreasing at f(x) is concave up at f(x) is concave down at B C D Sketch the graph of a function having the given properties. 2) From x = 0 to x = 10 the function increases and the slope decreases. When x > 10 the function decreases and the slope decreases (note: the slope is negative and becomes more negative). 3) Sketch the graph of a function with the following properties: I. f(x) > 0, for x x2 - 10x occur. Distinguish the maxima from the minima using the second derivative rule