Math 1210 Signature Assignment

The Mean Value Theorem

Begin by making a complete statement of the mean value theorem.

Consider the function on the interval [-3, 7].Explain how this meets the conditions of the Mean Value Theorem.

Find the average rate of change of on [-3, 7], and find the equation of the line segment that connects the points (-3, f (-3)) and (7, f (7)).

Find any numbers c, which are guaranteed by the Mean Value Theorem, and find the equation of the tangent line to the function at each value of c.Use exact values and show all work.

Using technology, graph the function and the above lines on the same axes.Choose an appropriate viewing window.Include the graph in your report.

Explain in layman's terms what the Mean Value Theorem tells us about rates of change referring to your graph as an example.Give one "real world" example of an application of the Mean Value Theorem.Your example should include the meaning or purpose of the Mean Value Theorem in the given context and an explanation of why it may be important in a real application.What problems did you encounter in completing the assignment? How did you troubleshoot them, if you did?What new skills or insights did completing the assignment give you?Cite any sources used.

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Expectations:

All signature assignments must be completely word processed, including using an equation editor for all mathematics.Hand-written work will not be graded.All mathematical steps must be shown and there must be narrative in place to explain your process to your reader.Any charts or graphs will also be computer generated.Your problem will be presented in a clear and logical way.A signature assignment should be an exposition of your finest work and presentation.

There are writing labs on campus for general writing help.For help using the equation editor in Microsoft Word go to https://www.youtube.com/watch?v=Cir8RXGTEq8

A copy of this assignment will be placed in your SLCC general education e-Portfolio.Math 1210 is a Quantitative Literacy (QL) general education course.See your syllabus for more information regarding e-Portfolios.