Construction of the Tangent to a ParabolaTo find the tangent line to a curve at a point P we first pick another point on the curve a little bit away from P. Call this point Q. Do this below by clicking "Another Point". Then connect these two points by a secant line (click "Secant Line"). The slope of this secant line can be computed since we know two points on the line. (click "triangle"). Move the slider to 0 and observe how the secant lines approaches a line that just touches the curve at a single point. This line is called the tangent line. (click "tangent line" to show the tangent line). In other words, the secant lines approach the tangent line as h heads to 0.
Jamie Mulholland |