How to Find the Linearization L(x) of the Function f(x) at x = 9?

To find the linearization L(x) of a function f(x) at a given point, we follow these steps:

1. Identify the function: You need to know the function f(x). Let’s say f(x) is a function that you have in mind.
2. Calculate the value of f at the point: Compute f(9), where 9 is the point at which we want to linearize the function.
3. Find the derivative: Determine the derivative f'(x). This will help us find the slope of the tangent line at the point x = 9.
4. Evaluate the derivative at the point: Calculate f'(9) to get the slope of the tangent line at this point.
5. Construct the linearization: The formula for the linearization L(x) at a point a is given by:

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

Plugging in our values, we can express this as:

L(x) = f(9) + f'(9)(x - 9)

Once you have calculated f(9) and f'(9), substitute them into the equation. The resulting expression will be the linearization of the function f(x) at x = 9.