How do you find the linearization of $f (x) = \frac{1}{\sqrt{2 + x}}$ $f(x) = 1/sqrt(2+x)$ at the point a=0?

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Answer 1 · 2018-03-26T15:30:15

Linearization is finding the linear approximation to a function at a given point $y=f(a)+f'(a)(x-a)$

$f'(x)=-1/2(2+x)^(-3/2)$
$f'(0)=-1/2(2+0)^(-3/2)=-0.18$
$f(0)=1/sqrt(2)=0.71$
$f(0)~=f(0)+f'(0)*(x-0)=0.71-0.18*x$

How do you find the linearization of f(x) = 1/sqrt(2+x)f(x)=1√2+xf(x) = 1/sqrt(2+x) at the point a=0?