Question

What information do you need to know about a function in order find its linear approximation near a point.

Answer 1

I am going to suggest Newton Method - which requires the roots of a function. A technique to figure out a good approximation for the tangent of a function at a certain point.

Answer 2

@rational @wio

Answer 3

Never mind. Ignore my previous response

Answer 4

You need the value of the the function and the value of its derivative at the point.

Answer 5

\[
\Delta y \approx \frac{dy}{dx}\Delta x\\
f(x) - f(a) \approx f'(a) \bigg(x-a\bigg)\\
L(x) = f'(a)\bigg(x-a\bigg) + f(a)
\]Where \(L(x)\) is the linear approximation of \(f(x)\) near \(x=a\).

Answer 6

can you explain this further, @wio