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Calculus/mean value theorem

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Expert: eigensteve - 7/1/2009


Question
Hi,I've been trying to solve this question about mean value theorem but it has me confused because it doesnt contain any values and is all in variables.
The questions is:
for the function f(x)=Ax˛+Bx+C, determine the value of c guarenteed by the mean value theorem on the interval [x₁,x₂}.

Answer
Hi Dan,

The idea is that the mean value theorem guarantees a point in the interval where the slope is equal to the "average" slope over the interval, determined by:

c = (f(x2)-f(x1))/(x2-x1)

So plug x1 and x2 into f(x) and determine what value of the slope is guaranteed at some point in the interval.

Hope this helps,

Steve

Calculus

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eigensteve

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Any questions about introductory or advanced calculus, real or complex analysis, linear algebra, or ordinary differential equations are fair game. I can answer questions about specific calculations, derivations, proofs, and physical applications. Your questions are as good for me as they are for you!

Experience

I use linear algebra and differential equations almost every day for my research on modeling unsteady aerodynamics. In particular, my research experience includes numerical integration of trajectories, stability analysis of fluid flow fields, numerical computation of Lyapunov exponents, and more.

Organizations
SIAM AIP APS AIAA IEEE

Publications
AIAA Aerospace Sciences Meeting and Exhibit [2008, 2009]. IEEE Photovoltaic Specialist [2009]. For these publications, see http://carlsbad.princeton.edu/~steve/papers/

Education/Credentials
I earned my B.S. in Mathematics from Caltech in 2006. I am currently a PhD. Candidate in Mechanical and Aerospace Engineering at Princeton. I expect to graduate in 2011.

Awards and Honors
Athena-Feron Scholarship Award for Excellence in Mathematical Coursework [2007], Princeton MAE Second Year Fellowship for Research Excellence [2007], Gordon Wu Fellowship [2006-2010], Caltech Summer Undergraduate Research Fellowship [2003-2005].

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