A Level Physics Practice Exam

Which of the following best describes the significance of drawing a tangent to a curve?

1. It helps find the average rate of change over the entire graph

2. It approximates the line of best fit for non-linear data

3. It provides the instantaneous rate of change at that point

4. It simplifies complex data into linear models

The correct answer is: It provides the instantaneous rate of change at that point

Drawing a tangent to a curve is significant because it provides the instantaneous rate of change at that specific point on the curve. The tangent line represents how the function behaves in an infinitesimally small interval around that point, allowing us to understand the slope or gradient precisely at that location. This is crucial in calculus, where the concept of a derivative is defined as the limit of the average rate of change as the interval approaches zero. In summary, the tangent line is an essential tool for analyzing how a function changes at a specific point, rather than over an interval, which is what other options may imply.