  HOME COURSES PREVIEW REVIEW ABOUT CONTACT Toll-Free Info & Ordering M-F: 9am-5pm (PST): (877) RAPID-10 24/7 Technical Support QUICK TOUR Member Login:  Rapid Courses Catalog Mathematics in 24 Hours Chemistry in 24 Hours Biology in 24 Hours Physics in 24 Hours Math Survival Weekly
Get the insider's tips and tricks in how to survive your math course and ace the next test. Subscribe the Web's only math weekly newsletter for students and learn:
- How to Study Math Effectively
- How to Take Math Courses Strategically
- How to Solve Math Problems Systematically
- How to Score High in Math Exams
- How to Master Math Rapidly

Enter your name and email below and get started today! Math Study Lounge These study sheets are for quick review on the subjects. Refer to our rapid courses for comprehensive review.     - Getting Started with Algebra     - Geometry Basics     - How to Solve Math Problems     - Trigonometry Quick Review     - Statistics At-A-Glance     - Calculus Preview Home » Calculus

Applications of Differentiation II-Inflection, Theorems
(MVT and Rolle’s) and Curve Sketching

 Topic Review on "Title": Rolle’s Theorem: If is continuous over and differentiable over and if then there is at least one number in such that The Mean Value Theorem: If is continuous over and differentiable over , and if then there is at least one number in such that Definition of the second derivative of a function: The second derivative is the derivative of the derivative of a function. First Derivative Test: If is a function continuous on and differentiable on then: If for all in then f is increasing on If for all x in then f is decreasing on If for all x in then f is constant on Second Derivative Test: If f is a function continuous on and differentiable on then: If for all x in then is concave up on If for all x in then is concave down on If for all x in then is changing concavity on Concavity: Curvature of a line or object, represented by the focus of the points on that region. Concave upward: Curvature such that the “bowl” of the curvature is directed upwards, or the focus is above the curve. Concave downward: Curvature such that the “bowl” of the curvature is directed downwards, or the focus is below the curve.

Rapid Study Kit for "Title":
 Flash Movie Flash Game Flash Card Core Concept Tutorial Problem Solving Drill Review Cheat Sheet   "Title" Tutorial Summary : This tutorial discusses Rolle’s Theorem and the Mean Value Theorem with the help of examples and graphical representation of the concepts on hand. Learning how to take second order derivatives is discussed in this tutorial. The use of second derivatives to find possible points of inflections is covered in this tutorial. The knowledge attained so far about curve sketching and their properties is mentioned in this tutorial. The usage of the Mean Value and Rolle’s Theorem is covered in some sections of this tutorial. Taking higher order derivatives requires a deeper understanding of the second derivative and its generality. The first and second derivative tests are covered in this tutorial.

 Tutorial Features: Specific Tutorial Features: Animated diagrams showing the first and second derivative tests. Graphic organizers to illustrate the inflection points of a function and the different types of concavity covered in this tutorial. Series Features: Concept map showing inter-connections of new concepts in this tutorial and those previously introduced. Definition slides introduce terms as they are needed. Visual representation of concepts Animated examples—worked out step by step A concise summary is given at the conclusion of the tutorial.

 "Title" Topic List: ```Rolle’s Theorem and the Mean Value Theorem Taking Higher Order Derivatives Points of Inflection- An application of the second derivative Concavity and its different types Curve Sketching ```

See all 24 lessons in Calculus, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Calculus Visually in 24 Hours

 ©2014 Rapid Learning Center. Privacy Policy | Disclaimer Chemistry Survival Publishing, Biology Survival Publishing and Physics Survival Publishing are the divisions of Rapid Learning Inc.