I want to know how to find the local linearization. So in this problem I'm doing, I'm given the f(x) equation and it says "about x = 0" I'm suppose to approximate value of f(0.3)

Question

Are there specific steps I need to take to go about this problem?

Answer 1

you want the tangent line to the curve at x=0.

In a small neighborhood, the curve will stay close to the tangent line. (In fact, any curve is "straight" in a small enough interval!)

So, you know that at x=0.3, the curve will be fairly close to the tangent line, which may be used to approximate the value of f(0.3). So, get the tangent line, and then plug in x=0.3 into the tangent line, not f(x).

Naturally, the tangent line at (h,k) is

y-k = y'(h) (x-h)