Exploring the Derivative at a Point

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Type:

Graphic Organizer/Worksheet

Description:

<p>To learn the alternate definition of a derivative at a point, students will plug the f<img src="/xwiki/resources/icons/silk/cancel.gif" class="wikimodel-freestanding" alt="cancel"/>=sqrt<img src="/xwiki/resources/icons/silk/cancel.gif" class="wikimodel-freestanding" alt="cancel"/> into the definition.  With algebra techniques like either the difference of squares or rationalizing the numerator, they will discover the derivative.  This worksheet should be given to groups of 3 or 4 to discuss their way through it and understand it both graphically & analytically.  Hat tip to the works of Paul Foerster!</p>

Subjects:

Mathematics > General

Education Levels:

Grade 11
Grade 12
Higher Education
Graduate
Undergraduate-Upper Division
Undergraduate-Lower Division

Keywords:

calculus differentiation derivative defintion square root function exploration inquiry discovery limit slope tangent

Language:

English

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Public - Available to anyone

License Deed:

Public Domain

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To learn the alternate definition of a derivative at a point, students will plug the f cancel =sqrt cancel into the definition. With algebra techniques like either the difference of squares or rationalizing the numerator, they will discover the derivative. This worksheet should be given to groups of 3 or 4 to discuss their way through it and understand it both graphically & analytically. Hat tip to the works of Paul Foerster!