Created on: October 31, 2014

Website Address: https://library.curriki.org/oer/AD2-Find-a-tangent-line-to-a-curve-at-a-point-and-a-local-linear-approximation

TABLE OF CONTENTS

- Curriki Project Based Geometry
- Curriki Calculus: Applications of Derivatives
- Curriki Calculus: Integrals

- Selling Geometry
- Designing a Winner
- What's Your Angle, Pythagoras?
- TED Talk: House of the Future
- The Art of Triangles
- How Random Is My Life?
- Introduction to Angles
- Lesson -- Drawing right triangles from word problems
- Accessing Curriki Geometry Projects
- Introduction to Curriki Geometry

- Selling Geometry Resources
- Curriki Geometry Tools and Resources
- Lesson -- Rotation
- The World Runs on Symmetry
- Lesson -- Dilations and Isometry
- Lesson -- Composition of Transformations
- Cool Math 4 Kids: Tessellations
- Tessellations.org
- Euclid
- About Cloze Notes
- What's the point of Geometry? - Euclid
- Selling Geometry Project Teacher Edition
- Selling Geometry Project Student Packet

- Applications of Derivatives Table of Contents by Standard
- AD.1: Find the slope of a curve at a point.
- AD.2: Find a tangent line to a curve at a point and a local linear approximation.
- AD.3: Decide where functions are decreasing and increasing.
- AD.4: Solve real-world and other mathematical problems involving extrema.
- AD.5: Analyze real-world problems modeled by curves.
- AD.6: Find points of inflection of functions.
- AD.7: Use first and second derivatives to help sketch graphs.
- AD.8: Compare the corresponding characteristics of the graphs of f, f', and f".
- AD.9: Solve optimization real-world problems with and without technology.
- AD.10: Find average and instantaneous rates of change.
- AD.11: Find the velocity and acceleration of a particle moving in a straight line.
- AD.12: Model rates of change, including related rates problems.
- AD.13: Interpret a derivative as a rate of change in applications.
- AD.14 Geometric interpretation of differential equations via slope fields

- How to Determine Relative Extrema on the Graphing Calculator
- Optimization Problems
- Solving Optimization Problems
- Optimization: Example 1
- Optimization: Example 2
- Optimization: Example 3
- Optimization: Example 5 (harder)
- Derivatives Using TI Calculator
- Optimization: Maximizing Volume
- Optimization Exercises
- Some Max-Min Problem Exercises

- Derivatives and Tangent Lines
- The Derivative
- Estimating a Function Value Using the Linear Approximation
- Find slope & equation of tangent line at a given point
- Tangent Line Approximation
- Slopes of Tangent Lines via Limits Exercises
- Tangent Lines Exercises
- Tangent Lines and Normal Lines Exercises
- Some Differentiation Formulas Exercises

Find a tangent line to a curve at a point and a local linear approximation.

A Youtube Calculus Workbook (Part 1). A guide through a playlist of instructional Calculus Videos. Sect 3.8 pp 59-61, Sect 5.4, pp 78-80, Sect 6.3 pp 87-88, Sect 6.7, pp 94-95, Sect 7.1-2, pp 101-105The first time you access this link to download the PDF, you will be asked four questions. Any that do not apply to you may be answered using any of the options listed.

Online text describing how to: Demonstrate an understanding of the derivative of a function as a slope of the tangent line. Demonstrate an understanding of the derivative as an instantaneous rate of change. Understand the relationship between continuity and differentiability.

MIT Open Courseware video on this topic

A Youtube video on this topicVideo duration: 9:50

Firefly Lectures video on this topicVideo duration: 11:12

Mooculus Calculus Textbook Sect 3.1, p 53-54 (Ans. p 247)This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.8 Look for and express regularity in repeated reasoning.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.

This set of exercises supports the following Standards of Mathematical Practice1 Make sense of problems and persevere in solving them.2 Reason abstractly and quantitatively.5 Use appropriate tools strategically.6 Attend to precision.7 Look for and make use of structure.