Explain the relationship between a function and the derivative by providing an example.

What is another name for the derivative when looking at a function graphically? A triangle that must contain pairs of points whose slopes are the opposite, reciprocal of each other is what kind of triangle? And what would we say the lines are to each other?

The graph attached shows the curves y = x^3 and y^3=x. a.) Explain why both of these curves are functions. b.) For the curve y^3=x, write y as a function of x.