Differentiation - secant gradient function

A secant gradient function gives the gradient of a secant at every point on a curve.

Consider the curve y = x² .

Suppose we draw each secant using an increase in x of 0.1.

Use the graphics calculator to draw the graph of y = x² and the secant gradient function.

Try x-increment values smaller than 0.1.

As the value of the x-increment gets closer to 0, the secant gradient function gets closer to 2x.

Use the graphics calculator to draw the graph of y = x³ and the secant gradient function.

Try x-increment values smaller than 0.1.

As the value of the x-increment gets closer to 0, the secant gradient function gets closer to 3x².

nDeriv on the TI-83 (built-in secant gradient function)
For an x-increment of 0.1, the value of nDeriv for y = x³ is calculated as .

• What does the diagram look like for such a secant?
• Is this method of drawing the secant better than the one shown above?