# Ch 43: Praxis Mathematics: Optimization and Differentiation

### About This Chapter

## Praxis Mathematics: Optimization and Differentiation - Chapter Summary

This chapter's lessons will prepare you for Praxis Mathematics exam questions that cover optimizing simple and complex systems. You will learn to solve applied minima-maxima problems and use relative maxima and minima to analyze the behavior of a function. Another lesson will lead you through an examination of optimization and differentiation. Topics covered in this chapter include:

- Optimizing complex systems
- Optimizing simple systems
- Optimization and differentiation

Expert instructors guide you through these videos, and they know how to make the lessons both informative and entertaining. You will enjoy yourself as you gain knowledge and prepare for the test. Before moving on to the next lesson, be sure to take the self-assessment quiz that follows each lesson.

### Objectives of the Praxis Mathematics Course

Many states require the Praxis Mathematics test for individuals who want to teach math at the secondary school level. There are 50 multiple-choice questions on the Praxis Mathematics test, and you will be allotted two hours to complete it. The topics covered in this optimization and differentiation chapter are included in the test's calculus section. This section has six questions, which constitutes about 12% of the test as a whole.

On the Praxis, you'll be presented with a problem and four choices of answers from which to choose. You can check your knowledge and get accustomed to the test's format by taking the self-assessment quizzes that accompany each video lesson.

### 1. 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.

### 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. 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.

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### Other Chapters

Other chapters within the Praxis Mathematics - Content Knowledge (5161): Practice & Study Guide course

- Praxis Mathematics: Counting Numbers Properties
- Praxis Mathematics: Rational and Irrational Numbers
- Praxis Mathematics: Solving Problems with Reasoning
- Praxis Mathematics: Percents
- Praxis Mathematics: Ratios and Proportions
- Praxis Mathematics: Scientific Notation & Order of Magnitude
- Praxis Mathematics: Algebraic Expressions
- Praxis Mathematics: Algebraic Equations
- Praxis Mathematics: Algebraic Fractions
- Praxis Mathematics: Linear Equations
- Praxis Mathematics: Systems of Equations
- Praxis Mathematics: Radicals Operations
- Praxis Mathematics: Exponents
- Praxis Mathematics: Distance
- Praxis Mathematics: Functions
- Praxis Mathematics: Inverse Functions
- Praxis Mathematics: Logarithmic Functions
- Praxis Mathematics: Rational Functions
- Praxis Mathematics: Complex Numbers Operations
- Praxis Mathematics: Sequences, Series & Probability
- Praxis Mathematics: Combinations & Permutations
- Praxis Mathematics: Quadratic Equations
- Praxis Mathematics: Polynomials
- Praxis Mathematics: Matrix Algebra
- Praxis Mathematics: Algebraic Formulas
- Praxis Mathematics: Measurement
- Praxis Mathematics: Area
- Praxis Mathematics: Polygons
- Praxis Mathematics: Quadrilaterals
- Praxis Mathematics: Circles
- Praxis Mathematics: Triangles
- Praxis Mathematics: Congruence, Similarity and Transformations
- Praxis Mathematics: Three-Dimensional Space and Volume
- Praxis Mathematics: Data
- Praxis Mathematics: Distributions
- Praxis Mathematics: Graphing
- Praxis Mathematics: Trigonometry
- Praxis Mathematics: Continuity
- Praxis Mathematics: Asymptotes
- Praxis Mathematics: Limits
- Praxis Mathematics: Derivatives
- Praxis Mathematics: Integrals
- Praxis Mathematics: Theorems
- Praxis Mathematics: Statistics
- Praxis Mathematics: Interpreting Statistics
- Praxis Mathematics: Understanding Logic
- Praxis Mathematics: Content Knowledge Flashcards