Question

Find the Linearization of f(x, y) at the Point

What mathematical concept involves finding the linear approximation of a multivariable function at a specific point?

A) Tangent Plane Calculation
B) Linear Regression
C) Multivariate Expansion
D) Function Approximation

Answer 1

The mathematical concept that involves finding the linear approximation of a multivariable function at a specific point is Tangent Plane Calculation (option A).

Step-by-step explanation:

The mathematical concept that involves finding the linear approximation of a multivariable function at a specific point is Tangent Plane Calculation (option A).

In calculus, the tangent plane calculation is used to find the linear approximation of a multivariable function at a given point. This involves finding the equation of the tangent plane to the surface represented by the function at that point. The tangent plane serves as a linear approximation to the function near the point of interest.

For example, if you have a function f(x, y), the linearization at a specific point (a, b) is given by:

f(x, y) ≈ f(a, b) + fx(a, b)(x - a) + fy(a, b)(y - b)