## anonymous 5 years ago find the linearization of f(x) = 1/x at a=10

1. anonymous

The linearization of a function can be found using the following method: $f(x) ≈ f(a)+f\prime(a)(x-a)$ Where f(a) = 1/a f'(a) = d/dx(1/a) So, all we have to do is compute the derivative of f(x) and then we have everything we need to get the linearization. $f(x) = 1/x = x^{-1}$$f\prime(x)=-x^{-2}=-1/x^{2}$ Now we just apply the rule to approximate the tangent line at x=a=3 so, $f\prime(a) = -1/(3)^{2} = -1/9$$f(a) = 1/a = 1/3$ Therefore, the linear approximation of f(x) at a = 3 is $f(x) ≈ 1/3 - 1/9(x - 3)$ Now will you go on a date with me? :P

2. anonymous

haha if your answer turns out to be correct? ;)

3. anonymous

how would i use this to approximate 1/9.78 just plug that in for x?

4. anonymous

Yup, smart and beautiful.

5. anonymous

haha hardly smart if i'm on this thing but thank you