# Ch 29: PLACE Mathematics: Applications of Derivatives

### About This Chapter

## PLACE Mathematics: Applications of Derivatives - Chapter Summary

The Program for Licensing Assessments for Colorado Educators (PLACE) Mathematics exam covers a variety of mathematical topics necessary for prospective math teachers to know. This chapter will help you review information on the applications of derivatives, including:

- Differentiation and optimization
- Optimizing simple systems
- Optimizing complex systems

If you become confused about any of the topics in these lessons, ask our instructors any questions you may have to get the most out of this chapter. You can also complete lesson lesson quizzes to find areas you don't understand. Go through and review these areas with video tags that will take you to key points in the video lessons.

### PLACE Mathematics: Applications of Derivatives Chapter Objectives

The PLACE Mathematics certification exam is a paper based, multiple-choice question test, for which test takers are given 4.5 hours to complete. Of the topics covered by this exam, 19% of the test is on calculus and discrete mathematics. This chapter has been compose to help you review the applications of derivatives.

### 1. Optimization and Differentiation

Optimization is the process of applying mathematical principles to real-world problems to identify an ideal, or optimal, outcome. Learn to apply the five steps in optimization: visualizing, definition, writing equations, finding minimum/maximums, and concluding an answer.

### 2. Optimizing Simple Systems

Most optimization problems involving simple systems can be solved using the five-step method. Explore how to solve optimization problems using these five steps: visualizing, defining the problem, writing the equation, finding the minimum or maximum, and answering the question.

### 3. Optimizing Complex Systems

Optimizing complex system starts by using a five-step system that is taught in mathematics; define the problem, write an equation for it, find the minimum or maximum for the problem and answer the questions. Learn more on the five steps to optimizing complex systems.

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### Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

- PLACE Mathematics: Properties of Real Numbers
- PLACE Mathematics: Fractions
- PLACE Mathematics: Decimals & Percents
- PLACE Mathematics: Ratios & Proportions
- PLACE Mathematics: Measurements & Conversions
- PLACE Mathematics: Logic
- PLACE Mathematics: Mathematical Reasoning
- PLACE Mathematics: Vector Operations
- PLACE Mathematics: Matrices & Determinants
- PLACE Mathematics: Exponents & Exponential Expressions
- PLACE Mathematics: Algebraic Expressions
- PLACE Mathematics: Linear Equations
- PLACE Mathematics: Inequalities
- PLACE Mathematics: Absolute Value Problems
- PLACE Mathematics: Quadratic Equations
- PLACE Mathematics: Polynomials
- PLACE Mathematics: Rational Expressions
- PLACE Mathematics: Radical Expressions
- PLACE Mathematics: Systems of Equations
- PLACE Mathematics: Complex Numbers
- PLACE Mathematics: Functions
- PLACE Mathematics: Graphing Piecewise Functions
- PLACE Mathematics: Exponential and Logarithmic Functions
- PLACE Mathematics: Continuity of Functions
- PLACE Mathematics: Limits
- PLACE Mathematics: Rate of Change
- PLACE Mathematics: Calculating Derivatives & Derivative Rules
- PLACE Mathematics: Graphing Derivatives & L'Hopital's Rule
- PLACE Mathematics: Area Under the Curve & Integrals
- PLACE Mathematics: Integration & Integration Techniques
- PLACE Mathematics: Integration Applications
- PLACE Mathematics: Foundations of Geometry
- PLACE Mathematics: Introduction to Geometric Figures
- PLACE Mathematics: Properties of Triangles
- PLACE Mathematics: Triangles, Theorems & Proofs
- PLACE Mathematics: Parallel Lines & Polygons
- PLACE Mathematics: Quadrilaterals
- PLACE Mathematics: Circular Arcs & Circles
- PLACE Mathematics: Conic Sections
- PLACE Mathematics: Geometric Solids
- PLACE Mathematics: Analytical Geometry
- PLACE Mathematics: Using Trigonometric Functions
- PLACE Mathematics: Trigonometric Graphs
- PLACE Mathematics: Solving Trigonometric Equations
- PLACE Mathematics: Trigonometric Identities
- PLACE Mathematics: Sequences & Series
- PLACE Mathematics: Graph Theory
- PLACE Mathematics: Set Theory
- PLACE Mathematics: Overview of Statistics
- PLACE Mathematics: Summarizing Data
- PLACE Mathematics: Tables & Plots
- PLACE Mathematics: Probability
- PLACE Mathematics: Discrete Probability Distributions
- PLACE Mathematics: Continuous Probability Distributions
- PLACE Mathematics: Sampling
- PLACE Mathematics: Hypothesis Testing
- PLACE Mathematics: Regression & Correlation
- PLACE Mathematics Flashcards