1. Consider the function f(x) = 2x3 - 3x2 - 36x a. Find the intervals of increase or decrease. Use a sign chart. b. Find the local max and min value points. c. Find the intervals of concavity and inflection points. Use a sign chart. d. Using parts (a) to (d), sketch the graph of f(x) indicating all local extrema and inflection points.2. If 1200 cm of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Be sure to find the domain and use the ideas of section 4.7.3. A retailer has been selling 1200 computers a week at $350 each. The marketing department did research and believes that 1280 computers will be sold each week if the price is dropped to $340 each. (a) Find the demand function and its domain. Assume it is linear. (b) If the weekly cost function is C(x) =35, 000+120x , what should the price be set at to maximize profit