3B-2. Linear Approximation
Instructions:
On the Left Side:
- Use the input box for f(x) to define the function.
- Use the input box for c to adjust the location of the point P.
- Use the input box for dx to adjust the location of the second point (Q).
- Check the Error checkbox to show/hid the error.
- Use the slider tool for dx to visualize the horizontal change in x.
- Use the slider tools for and dy to visualize the change in y along the function and along the tangent line, respectively.
- Use the Zoom In / Zoom Out buttons as needed.
Linear Approximation
The linearization of a function gives us a linear function that can be used to estimate the values of the function near the center of the linearization.
When x is close enough to c, this linearization gives a good estimate of f(x). That is,