^.^'s question at Yahoo Answers (Linearization)

[Fernando Revilla]

Here is the question:

Find the linearization L(x) of the function f(x)= ln (4x) at x = 1/4

Thanks!

Here is a link to the question:

http://answers.yahoo.com/question/i..._MUUqvfFDH1G;_ylv=3?qid=20130409181158AAxlDNJ

I have posted a link there to this topic so the OP can find my response.

 

[Fernando Revilla]

Hello ^.^,

Deriving: $f'(x)=\dfrac{4}{4x}=\dfrac{1}{x}$, so $f'(1/4)=\dfrac{1}{1/4}=4$. Now by definition of $L$, $$L(1/4):\mathbb{R}\to \mathbb{R}\\L(1/4)(h)=f'(1/4)h=4h$$ Or in classical notation, $L(1/4)\;(dx)=4\;dx$.

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