# Limit Definition of a Derivative

## Move the blue point (x, f(x)) around and notice how the blue and red lines move.

What does the red line represent? What does the blue line represent?

## Slowly move the blue point (x, f(x)) closer and closer to the red point (x+h, f(x+h)).

What is happening to the value of h as you move the blue point closer to the red point?

## Look at the limit definition of a derivative that is in the top left corner of the activity.

What does the f(x+h) represent? What does the f(x) represent? What is happening to those two values in the formula?

What does the h in the denominator represent?