# t2 - tires in storage, amount to \$4 per year for one tire....

This preview shows page 1. Sign up to view the full content.

Methods of Calculus MAC2233 Test 2 October 12, 1990 (1) (15 pts.) Sketch the graph of a function that has the properties: ( - 3 , - 2) and (1 , 4) are on the graph; f 0 ( - 3) = 0 and f 0 (1) = 0; f 00 ( x ) > 0 for x < - 1; f 00 ( - 1) = 0; and f 00 ( x ) < 0 for x > - 1. (2) (25 pts.) Sketch the graph of the function y = 2 x 3 - 6 x 2 - 48 x + 5, indicating all relative extreme points and inﬂection points. (3) (15 pts.) Consider the problem of ﬁnding the dimensions of the rectangular garden of area 111 square feet for which the amount of fencing needed to surround the garden is as small as possible. (a) Draw a picture of a rectangle with width w and length l . (b) Express the quantity to be minimized as a function of w . (4) (15 pts.) The Great American Tire Company expects to sell 600,000 tires of a particular size and grade during the next year. Sales tend to be roughly the same from day to day. Setting up each production run costs the company \$20,000. Carrying costs, based on the average number of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: tires in storage, amount to \$4 per year for one tire. (a) Determine the costs incurred if there are 20 production runs during the year. (b) Express the total inventory cost as a function of the production run size. (5) (15 pts.) Some years ago, it was estimated that the total demand for steel approximately satisﬁed the demand equation p = 88-20 x , and the total cost of producing x units of steel was C ( x ) = 175+8 x . (The quantity x was measured in millions of tons and the price and total cost were measured in millions of dollars.) Determine the level of production and the corresponding price that maximizes the proﬁts. (6) (15 pts.) Calculate the derivatives of the following functions. (a) f ( x ) = ± x x 2 + 1 ¶ 2 (b) g ( x ) = 2( x 3-1)(3 x 2 + 1) 4 (c) h ( x ) = 4 x 2 + x √ x 1...
View Full Document

## This note was uploaded on 07/13/2011 for the course MAC 2233 taught by Professor Staff during the Spring '08 term at FAU.

Ask a homework question - tutors are online