Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
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Factoring Rational Expressions Rational Equations and Applications
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15.Functions of Several Variables
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S = contains supplemental resources
Course: Calculus I
Topic: Analysis of Curves
Subtopic: Optimization Applications

Overview

Optimization is a process where we use calculus to find the maximum or minimum of a function that is subject to certain constraints. These applications are prevalent in STEM. For instance an engineer may need to minimize the use of steel by designing a bridge to be strong and efficient yet under certain constraints such as its length, the forces it will hold, and the geography of the area in which it will lie.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.7.1 Set-up an optimization application problem including finding the (often multivariate) function to be minimized/maximized and the constraint equation
• 3.7.2 Use the constraint equation to re-write the function to be minimized/maximized as a single-variable function
• 3.7.3 Use the derivative to minimize/maximize the function
• 3.7.4 Do all the steps necessary to solve an optimization application problem

Terminology

Define: optimize, optimization, constraint, constraint equation

Supplementary Resources (optional)