Practice Changing Rate in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

A changing rate of change means the output grows by different amounts for equal increases in input — the hallmark of nonlinear functions like quadratics and exponentials.

Changing rate means accelerating or decelerating progress — like compound interest where each year's gain is larger than the last because the base keeps growing.

Example 1

easy
For f(x) = x^2, compute the average rate of change on [1, 3] and on [1, 2], and explain why these differ.

Example 2

hard
For g(x) = x^3, find the average rate of change on [a, a+h] and simplify to see what happens as h \to 0.

Example 3

easy
A ball is thrown upward. Its height (m) is h(t) = -5t^2 + 20t. Find the average rate of change from t=0 to t=2 seconds.

Example 4

medium
Explain why the average rate of change of f(x) = |x| from x=-2 to x=2 is 0, even though f is not constant on that interval.
← Back to Changing Rate Worked Examples Formula Explained