# Drawing a Tangent to a Position-Time Graph

- Author:
- Andy Miller

- Topic:
- Calculus, Mathematics

The following interactive animation shows a "Calculus-like" approach to drawing the tangent to a position-time graph, especially along curved sections. The first step of the strategy is to align your straight-edge (ruler) with the targeted point of tangency and another point on the curve. Then as you move the second point to coincide with the targeted point of tangency, the ruler will go from tracing a secant (passing through two points on the curve) to tracing a tangent (touching one point on the curve in a small neighbourhood of points around it). Note that the second point can approach the targeted point of tangency from either side. The need to do so depends on whether you want the slope of the tangent as part of the interval to the right or to the left. In this case, the tangent's slope is the same as you make the second point approach the targeted point of tangency from either side.
Press play in the middle of the box below if you're on a mobile device, then press play in the lower-left corner of the box below to start the animation. After a few oscillations, stop the animation at h=0 to see the tangent line to the curve at t=1s.