Question #102a4

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Answer 1 · 2014-11-05T09:58:34

Linearization of f(x) at a

#L(x)=f(a)+f'(a)(x-a)#

Let us find the linearization #L(x)# of #g(x)# at #1#.

Since #g(1)=-3# and #g'(1)=sqrt{(1)^2+8}=3#,

#L(x)=g(1)+g'(1)(x-1)=-3+3(x-1)=3x-6#.

So, we can approximate:

#g(0.9) approx L(0.9)=3(0.9)-6=-3.3#

#g(1.1) approx L(1.1)=3(1.1)-6=-2.7#

I hope that this was helpful.