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I know the basic definition of the MVT, but I'm having alot of trouble applying it to this problem. I would greatly appreciate any kind of help or guidance.

A graph of the derivative of f(x) is displayed below. Information about the function f(x) is known only for -2.5 < x < 3.5. Also f(-2) = 1. Consider the graph carefully, and consider the information in both the numbers and the shapes of the graph (both "quantitative" and "qualitative" information).

the graph:

http://img148.imageshack.us/img148/5224/graphfx6.jpg [Broken]

a) Explain why -2 < f(0) < -1. Look carefully at the graph and make estimates using the MVT. Explain the steps of your reasoning in detail.

b) Explain why f(3) > 4 +f(1). Again, use the MVT and explain your reasoning in detail.

c) How big and how small can f(1) - f(0) be?

d) Use the information in a), b), and c) to explain why f(3) must be positive.

e) Explain why f(x) = 0 must have a solution between 0 and 3. Use the IVT (intermediate value th.) and the

information obtained in previous parts of this problem.

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# Homework Help: Mean Value Theorem

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