Question

What is the formula for ∆y under the linearization concept?

Option 1: ∆y = mx + b
Option 2: ∆y = dy/dx
Option 3: ∆y = f'(x)∆x
Option 4: ∆y = ∆x/∆t

Answer 1

The correct formula for Δy in the context of linearization is Δy ≈ f'(x) Δx, which represents the change in the output of a function based on its derivative at a certain point and the change in the input.

Step-by-step explanation:

The student appears to be asking for the formula for Δy under the concept of linearization which is a technique in calculus. However, the expression Δy = Δx/Δt provided in the question does not seem to correspond to the concept of linearization directly as it represents a rate of change (perhaps velocity), not a change in the function value (output).

In linearization, we approximate a function near a certain point using its linear tangent. If we have a differentiable function y = f(x), the change in y (Δy) near a point x is approximately equal to the derivative of f at x (f'(x)) multiplied by the change in x (Δx). This is expressed as:

• Δy ≈ f'(x) Δx

This approximation becomes more accurate as Δx becomes smaller. The formula Δy = f'(x) Δx is the fundamental idea behind differential calculus and is used for predicting changes and constructing tangent lines.