Limits and Derivatives

Differentiation (Lesson 1/6)

1 / 26

How could we find the slope of a parabola? Unlike a line, the steepness of a parabola varies, so we need to interpret the steepness of the curve at a point. For instance, look at x=2 on the graph of f(x)=x2 below.

What can we tell about the slope at that point? What if we utilize our knowledge of the slope of a straight line to estimate the slope at x=2 by connecting it to a nearby point on the graph of f.

Here, we have come up with an estimate for the slope, but how can we improve our estimate?