Practice Rate of Change in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A measure of how quickly one quantity changes with respect to another; the ratio of the change in output to the change in input.
How much does the output change for each unit increase in input? That ratio is the rate of change.
Example 1
easyThe position of a particle at time t seconds is s(t) = 3t^2 - 2t + 1 metres. Find the average rate of change of position from t = 1 to t = 4, and the instantaneous rate of change at t = 2.
Example 2
mediumWater drains from a tank so that the volume remaining after t minutes is V(t) = 500 - 20t - t^2 litres (0 \leq t \leq 10). Find the rate at which water is draining at t = 3 minutes.
Example 3
mediumFind the average rate of change of f(x) = x^3 - 2x on [1, 3].
Example 4
easyFind the average rate of change of f(x) = x^2 + 3x from x = 0 to x = 5.
Example 5
mediumThe temperature in a room is T(t) = 20 + 5\cos\left(\frac{\pi t}{12}\right) degrees Celsius at time t hours. Find the instantaneous rate of change of temperature at t = 6.