Linearisatie en benadering

Linearization simplifies complex, non-linear functions by replacing them with linear models near reference points.

For example, consider a square root function whose value at an input of 4 gives an output of 2. This input serves as the reference point. But when the input is 4.1, then the square root function is difficult to evaluate exactly.

In such cases, linearization approximates the function near a reference point by using the tangent line at that point. This tangent line is defined by the function’s value at the reference point plus the product of its derivative at the reference point and the small change (x−a) from it.

To approximate the value at x equal to 4.1, this tangent line expression is used.

First, the function’s value and its derivative at a are calculated. Then, the difference between x and a is found.

Combining these three terms gives an approximate value.

This estimate closely matches the actual square root of 4.1, with minimal difference. It serves as a simple example to show how the method of linearization and approximation works when functions are too complicated to evaluate exactly.