Question

How do you find the linearization of `f(x) = 2 ln(x)` at the point a=1?

Answer 1

The linearization is the equation of the tangent line (often written in a particular form).

Explanation:

`f(x) = 2ln(x)` at `x=1`, f(1) = 0#

`f'(x) = 2/x`, so `f'(1) = 2`

We get the linearization (and the tangent line) using

`y - f(a) = f'(a)(x-a)`

In this case `y = 0 + 2 (x-1)` Rewrite to taste (or the taste of the person grading your work.)