1. 35 – Local Linearization No Calculator
Derivative Investigations
35 – Local Linearization No Calculator

2. 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).

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

4. 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).

5. 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.