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Calculus/Linearization

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Question
I was hoping for some help with an old question of mine (got it wrong on homework a while ago- was sick the day this material was taught- never quite got the question).

Find the linearization L(x) off(x)=3x^4-5x^3 at x=2

Answer
Hello Clark,

I gather you are taking calculus, since this is a standard calculus question.

The linearization is just the tangent line approximation at the point given.

So, we just need the equation of the tangent line to f(x) at x=2.

First, let's find the y-value at x=2 ==> y=f(2)=8, so the point of tangency is (2,8).

Now for the slope, f'(2).  f'(x)=12x^3-15x^2 ==> f'(2)=36.

The line with slope 36 though (2,8) ==> y-8=36(x-2) ==> y-8=36x-72 ==> y=36x-64.

Thus, L(x)=36x-64

A. Mantell

Calculus

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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