Parametric+derivatives+and+Second+derivatives

= PARAMETRIC DERIVATIVES AND SECOND DERIVATIVES =

=** SECOND DERIVATIVES **= The main thing to remember about 2nd derivatives is it's just deriving twice. Just take the answer you got from deriving the first time and derive it again.

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 * APPLICATIONS OF SECOND DERIVATIVES **

The second derivative of an equation can determine the concavity of the function at a certain point. Steps to determine concavity: 1) Find the second derivative of the function 2) solve the equation by plugging in a value for x to determine the concavity at a certain point 3) use the chart below to determine the concavity at the point = **PARAMETRIC DERIVATIVE** = = =

= **SECOND PARAMETRIC DERIVATIVE** =



media type="youtube" key="iNDW-j1K218" height="286" width="356" media type="youtube" key="sfydzm4a4gY" height="313" width="391" Thus the derivative of the parametric series is... And the 2nd derivative of the parametric series is...
 * Ex.1**


 * Ex.2**

Thus the derivative of the parametric series is...

And the 2nd derivative of the parametric series is... = PARAMETRIC SECOND DERIVATIVES media type="custom" key="5808013" align="center" = = **ALSO** =

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= = = HOW DID WE DO? =

Topic: Parametric and Second Derivatives of Parametric functions Group Members: Kelsey and Sara

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I like the mixed media as well as the precise mathematical notation. Some of the terminology, ie. Parametric series? Is a bit off. The quality of the videos could be a bit better, but I like the effort. Lacks a little thoroughness, in terms of explaining why the 2nd derivative is what it is. Overall nice effort. Could use some graphical representation of dy/dx in a parametric equation.

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= SOURCES! = http://www.youtube.com/watch?v=7ANhq51wjWM http://www.youtube.com/watch?v=c1N8zyVhWxM&feature=channel http://www.mecca.org/~halfacre/MATH/parametricder.htm The Textbook!

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