Mean value theorem???
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Posted by Karishma Choudhary 7 years, 11 months ago
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Kritika Trehan 7 years, 11 months ago
The Mean Value Theorem is one of the most important theoretical tools in Calculus. It states that if <i>f</i>(<i>x</i>) is defined and continuous on the interval [<i>a</i>,<i>b</i>] and differentiable on (<i>a</i>,<i>b</i>), then there is at least one number <i>c</i> in the interval (<i>a</i>,<i>b</i>) (that is <i>a</i> < <i>c</i> < <i>b</i>) such that
The special case, when <i>f</i>(<i>a</i>) = <i>f</i>(<i>b</i>) is known as Rolle's Theorem. In this case, we have <i>f</i> '(<i>c</i>) =0. In other words, there exists a point in the interval (<i>a</i>,<i>b</i>) which has a horizontal tangent. In fact, the Mean Value Theorem can be stated also in terms of slopes.
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