find the linearization of f(x) = 1/x at a=10

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Yup, smart and beautiful.

anonymous · Answer

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