Tangent

To estimate its gradient at a chosen point, draw a tangent that follows the curve’s direction there. Choose two clear, well-separated points on the tangent and use rise divided by run. The result is an estimate because the drawn tangent and readings from the graph may not be exact.

A tangent is a straight line drawn so that its direction matches the curve at the chosen point. Its gradient estimates the instantaneous rate of change at that point. Thus, a tangent to a distance–time curve estimates speed at one instant, while a tangent to a velocity–time curve estimates acceleration at one instant.

The radius drawn from the centre to that point of contact is perpendicular to the tangent. This turns a circle problem into a perpendicular-line problem: find the radius's gradient, take its negative reciprocal, and then form the line through the point of contact.