Calculus
Advanced

Mean Value Theorem

Guarantees a point where the tangent equals the average slope.

Formula

f′(c)=f(b)−f(a)b−af'(c) = \frac{f(b)-f(a)}{b-a}

Variables

a,bInterval
cPoint in (a,b)

Example

Some point matches the average rate

Did You Know?

The Mean Value Theorem guarantees that at some instant your speed exactly equalled your average speed — proof a speed camera can use.

theorem