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Unformatted text preview: P where the tangent line is parallel to the secant line AB . Another way to interpret the Mean Value Theorem is that there is a number at which the instantaneous rate of change is equal to the average rate of change over an interval. Example 3 of Section 4.2 (textbook): Example 5 of Section 4.2 (textbook): Theorem : If f ( x ) = 0 for all x in an interval ( a, b ), then f is constant on ( a, b ). Corollary : If f ( x ) = g ( x ) for all x in an interval ( a, b ), then fg is constant on ( a, b ); that is, f ( x ) = g ( x )+ c where c is a constant. The above corollary says that, if two functions have identical derivatives on an interval, they must dier by a constant. Example 6 of Section 4.2 (textbook): 1...
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 Fall '08
 Noohi
 Calculus, Mean Value Theorem

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