A How to Guide to OptimizationBy

Louis M. Calucci

5 Calculus A

What is Optimization?

• Optimization is the process of finding the maximum or minimum of a function.

• It uses the Calculus concept of derivatives, as well as the algebra concept of solving equations.

• While most calculators have the built-in ability to find a max or min, Optimization is an important skill to know.

Real-World Applications

• Optimizing techniques can be used in many job situations.

• With Optimization, one can find the maximum volume, the minimum cost, the maximum yield, etc.

Optimizing a Function: Step 1

• Find the derivative of the function.

• Use the chain, product, power, trig, etc. rules

• If a function is not provided, create one first. Just put the information given into an equation.

xxxy 235230 Ex:

52513062 2 xxy

Optimizing a Function: Step 2

• Find any maximums/ minimums by finding the zeroes of the derivative function.

• Remember that the endpoints could be solutions, too.

• A graph may help! (See Step 3)

298.16

525130620 2

x

xx

Optimizing a Function: Step 3

• Plot a graph of the function over the values indicated (example: [0,15])

• If a domain is not given, then find the x values over which the solution to the original function exists.

Zero

Optimizing a Function: Step 4

• Plug the zeroes of the derivative into the original function. Don’t forget to check the endpoints.

• The highest value will be the maximum, and the lowest value will be the minimum.

Maximum

This Concludes the Presentation

Louis Michael Calucci IV is an Advanced Placement student at Southern Regional High School. Proficient in math, science, and computer usage, he plans to attend Syracuse University in Fall 2000, majoring in Computer Science. His hobbies are reading, playing video games, building Lego models, and listening to the music of composer John Williams. A huge Science Fiction fan, he has incorporated the virtually unknown Cantina Band #2 song into this presentation, which was written by Williams and appeared in Star Wars IV: A New Hope.

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Louis M. Calucci