Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

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
• 3.7.5 Interpret the result of an optimization application problem including recognizing the reasonableness of the answer

Terminology

Terms you should be able to define: optimize, optimization, constraint, constraint equation

Mini-Lectures and Examples

Supplementary Resources (optional)

rev. 2020-11-09