Question

How do you find the linearization at x=1 of `y = 2/x`?

Answer 1

`L(x)=4-2x`

Explanation:

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

Here, `f(x)=2/x=2x^-1`, `a=1, f(a)=2.`

So, `f'(x)=-2/x^2, f'(1)=-2`, `(x-a)=(x-1)`

The linearization is then

`L(x)=2-2(x-1)`

`L(x)=2-2x+2`

`L(x)=4-2x`