Optimization Rizzi – Calc BC.

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Presentation transcript:

Optimization Rizzi – Calc BC

Quiz Recap When looking for absolute extrema on a closed interval, CHECK ENDPOINTS Check answers to make sure they’re in the given interval Check your basic algebra Graphs of f’ will continue to be important

Optimization Refers to finding maximum or minimum values of SOMETHING based on certain constraints. Key Words: Greatest profit Least cost Greatest voltage Optimum size Shortest distance

Simple Problem Using a piece of 8.5x11” paper, I want to cut out squares from each corner to create a box with maximum volume. How big should the squares be?

Guidelines for Optimization Identify all given quantities and all quantities to be determined. Draw a picture. Write a primary equation for the quantity that is to be optimized. Reduce the primary equation to be in terms of a single variable, using secondary equations if necessary. Determine the feasible domain for the primary equation. What makes sense? Determine the desired max or min value by using first and second derivative tests.

Try it! A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?

One more Which points on the graph of the function are closest to the point (0, 2)?

AP Question C