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Applications of Extrema

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Presentation on theme: "Applications of Extrema"— Presentation transcript:

1 Applications of Extrema
Lesson 6.2

2 A Rancher Problem You have 500 feet of fencing for a corral
What is the best configuration (dimensions) for a rectangular corral to get the most area One side of the rectangle already has a fence

3 Sample Problem Your assistant presents you with a contract for signature Your firm offers to deliver 300 tables to a dealer at $90 per table and to reduce the price per table on the entire order by $0.25 for each additional table over 300 What should you do? Find the dollar total involved in largest (smallest) possible transaction between the manufacturer and the dealer.

4 Solution Strategy Read the problem carefully From our problem
Make sure you understand what is given Make sure you see what the unknowns are From our problem Given 300 tables at $90 per table $0.25 reduction per table on entire order if > 300 Unknowns Largest possible transaction Smallest possible transaction

5 Solution Strategy If possible sketch a diagram From our problem
Label the parts From our problem Not much to diagram … More likely in a problem about the size of a box to minimize/maximize materials or volume x + 3 x 2x

6 Solution Strategy Decide on a variable to be maximized (minimized)
Express variable as a function of one other variable Be sure to find function domain From our problem T = transaction amount T = f(x) = ?

7 Solution Strategy To analyze the function, place it in Y= screen of calculator Check the table (♦Y) to evaluate the domain and range for setting the graph window

8 Solution Strategy Find the critical points for the function
View on calculator For our problem Use derivative tests to find actual points

9 Solution Strategy If domain is closed interval For our problem
Evaluate at endpoints, critical points See which value yields absolute max or min For our problem

10 Strategy Review Read carefully, find knowns, unknowns
Sketch and label diagram Determine variable to be max/min Express as function of other variable Determine domain Find critical points If domain is closed interval Check endpoints Check critical points

11 Practice Problem A fence must be built to enclose a rectangular area of 20,000 ft2 Fencing material costs $3/ft for the two sides facing north and south It costs $6/ft for the other two sides Find the cost of the least expensive fence

12 Assignment Lesson 6.2 Page 383 Exercises 5 – 33 odd


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