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Mean value theorem - Derivative Applications

Mean value theorem

The idea of the Mean Value Theorem may be a little too abstract to grasp at first, so let’s describe it with a real-life example. Let’s say that if a plane travelled non-stop for 15 hours from London to Hawaii had an average speed of 500mph, then we can say with confidence that the plane must have flown exactly at 500mph at least once during the entire flight. In this section, we will learn about the concept and the application of the Mean Value Theorem in detail.

Lessons

  • 1.
    Consider the function f(x)=2x35x1f\left( x \right) = 2{x^3} - 5x - 1 on the interval [0, 2].
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Mean value theorem

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