About This Chapter
Geometrical Applications of Differentiation - Chapter Summary
Our informative lessons on the geometrical applications of differentiation cover topics like functions and the signs of their derivatives and how to find critical points in calculus. You'll review the formula used to find the second derivative as well as indefinite integrals as anti-derivatives. Once you complete this chapter, you will be able to:
- Find maximum and minimum values using differentiation
- Use the equation for a normal line and a tangent line
- Curve sketch intercepts, asymptotes and derivatives
Our fun video and text lessons make learning about even the most challenging topics easy and enjoyable. After reviewing the lessons, take the multiple-choice quizzes that follow each lesson to make sure you've understood them. If you need to go back and review any portion of a video lesson, use the video tabs feature for quick maneuvering. We make it easy to study whenever works best for you with 24/7 mobile-friendly access to our study tools.
1. Functions & the Signs of Their Derivatives
Read this lesson to learn how you can use the derivative of a function to figure out what the function is doing at any point on the graph. Learn what to look for to determine whether the function is decreasing or increasing.
2. Finding Critical Points in Calculus: Function & Graph
This lesson develops the understanding of what a critical point is and how they are found. It explores the definition and discovery of critical points using functions and graphs as well as possible uses for them in the everyday world.
3. Finding the Second Derivative: Formula & Examples
In this lesson, you will learn the two-step process involved in finding the second derivative. Also, look at some examples to get your feet wet before jumping into the quiz.
4. Curve Sketching Derivatives, Intercepts & Asymptotes
This lesson presents a calculus-based procedure for graphing various types of functions. The methods used will be based on using derivatives, intercepts, and asymptotes for graphing functions.
5. Using Differentiation to Find Maximum and Minimum Values
If you are shot out of a cannon, how do you know when you've reached your maximum height? When walking through a valley, how do you know when you are at the bottom? In this lesson, use the properties of the derivative to find the maxima and minima of a function.
6. Normal Line: Definition & Equation
In calculus, a normal line is a line that goes through a point on a curve and is perpendicular with the tangent line at that point. In this lesson, you'll learn more about normal lines and how to find their equations.
7. Tangent Line: Definition & Equation
In this lesson, we explore the idea and definition of a tangent line both visually and algebraically. After learning how to calculate a tangent line to a curve, you will find a short quiz to test your knowledge.
8. Indefinite Integrals as Anti Derivatives
What does an anti-derivative have to do with a derivative? Is a definite integral a self-confident version of an indefinite integral? Learn how to define these in this lesson.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Geometric Representations of Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards