35 – Local Linearization No Calculator Derivative Investigations 35 – Local Linearization No Calculator

Below are the graphs of the function and tangent line Below are the graphs of the function and tangent line. Notice what happens as we zoom in the graph around (3, 0). The more we zoom in, the more the function acts like a line. As long as remain local to x = 3, we can use the tangent line to approximate the value of the original function. Let’s examine f(3.1).

Compute Compute Compute Add/subtract all values We can use local linearization to get an approximation of f(3.1).

Local linearization of f(x): Using a tangent line at x = a to approximate values of a function local to x = a. We can use the tangent line at x = 3 (local to 3.1) to approximate f(3.1).

The further away from x = a, the less accurate the approximation. It would not be appropriate to use the tangent line at x = 3 to approximate f(4). It would not be appropriate to use the tangent line at x = 3 to approximate f(2). Local linearization of f(x): Using a tangent line at x = a to approximate values of a function local to x = a.