A.3.6—Tangents and instantaneous rates

The gradient of a tangent gives the instantaneous rate at one point on a curve. The tangent should touch the curve locally, not simply connect distant data points.

Draw a small, well-positioned tangent, choose two far-apart points on that tangent, calculate rise/run and include the correct units.

A respiration curve that flattens has a smaller tangent gradient later, showing that the instantaneous rate is falling even if total oxygen uptake still rises.

A tangent is an estimate whose uncertainty depends on curve thickness, measurement scatter and how the line is drawn.