Practice Mean Value Theorem in Math

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

Quick Recap

If f is continuous on [a, b] and differentiable on (a, b), then there exists at least one point c in (a, b) where f'(c) = \frac{f(b) - f(a)}{b - a}

If you drive 150 miles in 2 hours, your average speed is 75 mph. The MVT says at some instant during the trip, your speedometer read exactly 75 mph. The instantaneous rate must equal the average rate at least once.

Example 1

easy
Verify the MVT for f(x) = x^2 on [1, 3] by finding the value of c.

Example 2

hard
Use the MVT to prove: if f'(x) = 0 for all x in (a, b), then f is constant on (a, b).

Example 3

easy
Find the value of c guaranteed by the MVT for f(x) = x^3 on [0, 2].

Example 4

medium
A car travels 120 miles in 2 hours. Explain why the MVT guarantees the car exceeded 60 mph at some instant.
← Back to Mean Value Theorem Worked Examples Formula Explained