Final answer:
In the context of linearization of a function at a point, the first step, 'top part 1', involves finding the derivative of the function, which is key to forming the equation of the tangent line and creating the linear approximation near that point.
Step-by-step explanation:
When discussing the context of linearization of a function f(x) at a point x=a, the 'top part 1' often refers to the first step that needs to be taken in this process. Answering the question provided, the correct option is A) Finding the derivative of f(x)
The linearization process involves approximating f(x) by a line (its tangent) near the point x=a. This is done in several steps:
- Find the derivative f'(x).
- Evaluate the derivative at x=a, yielding the slope of the tangent line.
- Evaluate the original function at x=a, finding the point through which the tangent passes.
- Construct the linear equation of the tangent using the point-slope form, which becomes the linear approximation or local linearization of f(x) near x=a.
The other options provided (Evaluating the function, Constructing the equation of the tangent line, and Calculating the integral) are steps that come after finding the derivative or concern different concepts in calculus.