Presentation on theme: "Section 5.4 I can use calculus to solve optimization problems."— Presentation transcript:
1 Section 5.4I can use calculus to solve optimization problems.
2 1. The sum of two nonnegative numbers is 20. Find the numbers (a) if the sum of their squares is to be as large as possible.Let the two numbers be represented by x and 20 – x.makes x = 10 a minimum.Maximum must occur at an endpoint.0 and 20
3 1. The sum of two nonnegative numbers is 20. Find the numbers (b) If the product of the square of one number and thecube of the other is to be as large as possibleLet the two numbers be represented by x and 20 – x.1220+_Max at 12, Min at 2012 and 8
4 1. The sum of two nonnegative numbers is 20. Find the numbers (c) if one number plus the square root of the other is as largeas possible.Let the two numbers be represented by x and 20 – x.therefore a max
5 A rectangular pen is to be fenced in using two types of fencing. Two opposite sides will use heavy duty fencing at $3/ftwhile the remaining two sides will use standard fencing at $1/ft.What are the dimensions of the rectangular plot of greatest areathat can be fenced in at a total cost of $3600?3x1yTherefore maxThe dimensions of a rectangular plot of greatest area are 300 x 900
6 3. A rectangular plot is to be bounded on one side by a straight river and enclosed on the other three sides by a fence. With 800 m of fence at your disposal, what is the largest area you can enclose?xyTherefore a maxThe largest area you can enclose is 80000
7 4. An open-top box with a square bottom and rectangular sides is to have a volume of 256 cubic inches. Find the dimensions that require the minimum amount of material.yxtherefore a min8 x 8 x 4