Local Linearity II

Using Local Linearity to introduce difference quotient and the derivative. A good way to introduce difference quotients and derivatives is to write the equation of the “line” you see when you zoom-in on a locally linear function. First: Ask your class to use their calculator or computer grapher to graph a function, say y =…

Local Linearity I

Certain graphs, specifically those that are differentiable, have a property called local linearity. This means that if you zoom in (using the same zoom factor in both directions) on a point on the graph, the graph eventually appears to be a straight line whose slope if the same as the slope (derivative) of the tangent…