About This Chapter
Curve Sketching in Precalculus - Chapter Summary
As you work through the lessons in this chapter, our experienced instructors will explain curve sketching and the use of the first and second derivatives. Learn to graph the derivative of any function solely by looking at the graph of the function and how to graph the normal line of a curve. Explore cups and frowns, and see how inflection points signify a change from one to the other.
You will be familiar with these precalculus concepts after working through the lessons in this chapter:
- Graphing derivatives
- Non-differentiable graphs of derivatives
- Concavity and inflection points and their relationship to differentiation
View the video and complete the short, multiple-choice quiz as you work through each lesson in this chapter highlighting curve sketching in precalculus math. The graphics and formulas in the lesson transcripts make review quick and easy. Once you have completed the lessons, the chapter exam offers an excellent opportunity to test what you have learned.
1. Graphing the Derivative from Any Function
When you know the rules, calculating the derivates of equations is relatively straightforward, although it can be tedious! What happens, though, when you don't know the function? In this lesson, learn how to graph the derivative of a function based solely on a graph of the function!
2. Non Differentiable Graphs of Derivatives
When I walk along a curve, I stand normal to it. That is, I stand perpendicular to the tangent. Learn how to calculate where I'm standing in this lesson.
3. Concavity and Inflection Points on Graphs
You might not think of a cup when you think of an awesome skateboard ramp. But I'm sure a really bad ramp would give you a frown, right? Learn about cups and frowns in this lesson on concavity and inflection points.
4. Understanding Concavity and Inflection Points with Differentiation
Put a little more meaning behind those cups and frowns. In this lesson, use the second derivative of a function to determine if it is concave up or concave down.
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Other chapters within the GRE Math: Study Guide & Test Prep course
- Functions in Precalculus
- Analytical Geometry in Precalculus
- Polynomial Equations in Precalculus
- Logarithms & Trigonometry
- Limits of Sequences & Functions
- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
- Indefinite Integrals in Calculus
- Definite Integrals in Calculus
- Additional Topics in Calculus
- L'Hopital's Rule, Integrals & Series in Calculus
- Analytic Geometry in 3-Dimensions
- Partial Derivatives
- Calculus: Min/Max & Integrals
- Algebra: Differential Equations
- Algebra: Matrices & Vectors
- Algebra: Determinants & Transformations
- Algebra: Number Theory & Abstract Algebra
- Additional Topics: Sets
- Additional Topics: Unions & Intersections
- Additional Topics: Graphing & Probability
- Additional Topics: Standard Deviation
- Additional Topics: Topology & Complex Variables
- Additional Topics: Trigonometry
- Additional Topics: Theorems, Analysis & Optimizing