describe connections between the average rate of change of a function that is smooth (i.e., continuous with no corners) over an interval and the slope of the corresponding secant, and between the instantaneous rate of change of a smooth function at a point and the slope of the tangent at that point Sample problem: Given the graph of shown below, explain why the instantaneous rate of change of the function cannot be determined at point . [The document prints the graph here: a function with a corner at point P.]