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Expert: eigensteve - 6/25/2009


Question
I need help with some problems in my class. I'll be able to do the rest if I can get help with one of them.
It states:

construct a linear approximation for the function at x = -1

y=x^4-3x^3+2x^2-x+7

Answer
Hi Melissa,

The derivative gives you a linear approximation, so first compute the derivative:

dy/dx = 4x^3-9x^2+5x-1

Now at x=-1 we have

dy/dx|{x=-1} = -19

This is the slope of our linear approximation at x=-1.

Finally, we need to know the function value at x=-1:

y(-1) = 14

So the linear approximations is:

y = 14 -19*(x+1)
 = -5 - 19x


Hope this helps!

-Steve

Calculus

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eigensteve

Expertise

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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