Estimating the Slope of a Tangent Line
- Author:
- numath
Estimating the Slope of a Tangent Line
Consider the tangent line to the function at the point A. The purple line is the actual tangent line. But how can we best estimate the slope of the tangent line?
The green line shows a line going through two points on either side of our point A, namely B and C. The red line shows a line going through our point A and a nearby point D. Which line has a slope that is closer to the slope of the actual tangent line?
Move the graph of the function around. As you do, the points will retain the same x-values, but their y-values will change so as to move along the function, and the lines will change accordingly, but each line will still be constructed the same way.
As you move the points around in this way, does either the red line or the green line consistently give the better estimate of the slope of the tangent line? Based on this, which method is better for estimating the slope of a tangent line: choosing two points on either side of point A, or choosing A and one point near it?