On the Left Side:[list][*]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.[/*][/list][br]On the Right Side: [list][*]Use the slider tool for dx to visualize the horizontal change in x. [/*][*]Use the slider tools for [math]\Delta y[/math] 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. [/*][/list]

The [b]linearization [/b]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. [br][br][math]L(x)=f(c)+f'(c)(x-c)[/math][br][br]When x is [i]close enough[/i] to c, this linearization gives a good estimate of f(x). That is,[br][br][math]f(x)\approx L(x)=f(c)+f'(c)(x-c)[/math]