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?