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?
The secant line. The tangent line.
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?
The value of h is approaching zero.
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?
The y-value (height) of the red point. The y-value (height) of the blue point. They are being subtracted.
What does the h in the denominator represent?
The distance between the x-values of the red and blue points.
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Information: Limit Definition of a Derivative