Apply a second derivative to identify a critical points as a local maximum, local minimum or saddle point for a function. You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 450 cm³. The material for the base of the box costs 7 cents/cm² and the material for the sides of the box costs 7 cents/cm². Find the dimensions for a box that will minimize the cost of the materials used to construct box. Please show your answers to at least 4 decimal places. width: height: cm cm

The total revenue for a product can be calculated as the area under the demand curve. Suppose that the demand curve for a certain wine (in dollars per liter) is given by the following, where is the demand in liters. Estimate the total revenue using rectangles of width 10 ters D(4) = ² -10q+267 for 0 sqs50 The approximate revenue using left endpoints is The approximate revenue using right endpoints is $ The approximate revenue using the average is $

Suppose the Supply function for a product is given as p=30+ 0.001x^2   and the Demand function is given as  p= 90-0.3x .  Sketch the graph of the two functions, for 0 ≤ x ≤ 300. Make sure to LABEL your x and y axes with their scales. Find the point of intersection between the two functions. You do not need to do this algebraically. Find the Consumer’s Surplus using calculus.