#### AD.2: Find a tangent line to a curve at a point and a local linear approximation.

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

### Derivatives and Tangent Lines

by Allen Wolmer

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 101-105
The 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.

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### The Derivative

by Allen Wolmer

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.

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### Estimating a Function Value Using the Linear Approximation

by Allen Wolmer

MIT Open Courseware video on this topic

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### Find slope & equation of tangent line at a given point

by Allen Wolmer

A Youtube video on this topic

Video duration:  9:50

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### Tangent Line Approximation

by Allen Wolmer

Firefly Lectures video on this topic

Video duration:  11:12

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### Slopes of Tangent Lines via Limits Exercises

by Allen Wolmer

Mooculus Calculus Textbook Sect 3.1, p 53-54 (Ans. p 247)

This set of exercises supports the following Standards of Mathematical Practice

• 1 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.
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### Tangent Lines Exercises

by Allen Wolmer

This set of exercises supports the following Standards of Mathematical Practice

• 1 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.
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### Tangent Lines and Normal Lines Exercises

by Allen Wolmer

This set of exercises supports the following Standards of Mathematical Practice

• 1 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.
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### Some Differentiation Formulas Exercises

by Allen Wolmer

This set of exercises supports the following Standards of Mathematical Practice

• 1 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.
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