Question

What is the formula for dy under the linearization concept?

Option 1: dy = dx/dt
Option 2: dy = ∆y/∆x
Option 3: dy = f'(x)dx
Option 4: dy = mx + b

Answer 1

The correct formula for dy under the linearization concept is 'dy = f'(x)dx', representing an infinitesimal change in the function due to an infinitesimal change in x.

Step-by-step explanation:

The formula for dy under the concept of linearization is Option 3: dy = f'(x)dx. This is based on the definition of the differential dy, which represents an infinitesimally small change in the function y as a result of an infinitesimally small change in x, multiplied by the derivative of the function f with respect to x. When we linearize a function at a point x, we are approximating it locally by its tangent line, and dy reflects the change along this tangent line due to a small change in x.