The Slope of a Parabola
What is the slope of y = x2?
Recall slope refers to the rate of change of a function. Begin by computing the slope between two points on the y = x2 function that are .001 units apart in the x-direction. Repeat the process for several (many) pairs of points. What happens to the slope? Organize your collection of data in a manner that may help a pattern stand out. Is there a pattern in your data that would help you predict the slope?
Extension:
Investigate the slope of a different curve in the form y = xn and compare findings and generalizations among your classmates.