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1. Be able to apply The Mean Value Theorem to various functions.
Objectives: 1. Be able to apply The Mean Value Theorem to various functions. Critical Vocabulary: The Mean Value Theorem Warm Up: Determine if Rolle’s Theorem can be applied. If it can, find all values of c such that f’(c) = 0. f(x) = x2 - 5x + 4; [1, 4]
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If f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that
![If f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that](http://slideplayer.com./slide/16900544/97/images/2/If+f+is+continuous+on+a+closed+interval+%5Ba%2C+b%5D+and+differentiable+on+the+open+interval+%28a%2C+b%29%2C+then+there+exists+a+number+c+in+%28a%2C+b%29+such+that.jpg "If f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that")
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Example 1: Given f(x) = 5 - (4/x), find all values of c in
the open interval (1,4) such that
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Example 2 (page 326 #24): Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that
![Example 2 (page 326 #24): Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b].](http://slideplayer.com./slide/16900544/97/images/4/Example+2+%28page+326+%2324%29%3A+Determine+whether+the+Mean+Value+Theorem+can+be+applied+to+f+on+the+closed+interval+%5Ba%2C+b%5D..jpg "If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that.")
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