![]() Additional examples illustrate some of the results that are based on the MVT. In place of a proof, examples will be provided to show how the MVT can fail to hold if the hypotheses are not satisfied. Some of the more important uses of the MVT are not so geometric and require more effort to understand. The geometric nature of the MVT makes it easy to believe and understand. ![]() The Mean Value Theorem (MVT) is one of the milestones in calculus. Return evalb( evalf(x)>=op(1,S) and evalf(x) Warning, the name changecoords has been redefined Example 5: Existence of a Unique Root in an Interval.Example 4: Geometric and Arithmetic Means.Example 3: The MVT and the Highway Patrol.Example 2: Using the MeanValueTheorem Maplet.Case 2: Hypotheses not satisfied: Function not continuous.Case 1: Hypotheses not satisfied: Function continuous but not differentiable.Example 1: A Closer Look at the Hypotheses of the MVT.
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