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4.2 The Mean Value Theorem State Standard
– 8.0b Students know and can apply The Mean Value Theorem Objective – To be able to use the Mean Value Theorem.
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The Mean Value Theorem connects the average rate of change of a function over an interval with the instantaneous rate of change of the function at a point within the interval.
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The Mean Value Theorem If f is continuous on the closed interval [a, b] and differentiable on the open (a, b) then there exist a # ‘c’ in (a, b) such that:
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Example 1
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Example 2
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Example 3
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Rolle’s Theorem Let f be continuous on the closed interval [a,b] and differentiable on the open (a,b). If f(a) = f(b) Then there is at least one # ‘c’ in (a,b) such that f’(c)=0
![Rolle’s Theorem Let f be continuous on the closed interval [a,b] and differentiable on the open (a,b). If.](http://slideplayer.com/slide/12693687/76/images/7/Rolle%E2%80%99s+Theorem+Let+f+be+continuous+on+the+closed+interval+%5Ba%2Cb%5D+and+differentiable+on+the+open+%28a%2Cb%29.+If..jpg "f(a) = f(b) Then there is at least one # ‘c’ in (a,b) such that f’(c)=0.")
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Example 1
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Example 2
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Example 3
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4.2 Assignemnt Pg. 295 11 – 14 and 1 – 4 (solve using the MVT)
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