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4.2 Mean Value Theorem
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How to differentiate Absolute Value
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Max’s, Min’s, Increasing, Decreasing
CP y y' x CP y y' Definitions & Corollary 1
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Mean Value Theorem If f is ______________ on [a,b] and _____________ on (a,b), then there is at least one c between a and b such that:
![Mean Value Theorem If f is ______________ on [a,b] and _____________ on (a,b), then there is at least one c between a and b such that:](http://slideplayer.com./slide/13828112/85/images/4/Mean+Value+Theorem+If+f+is+______________+on+%5Ba%2Cb%5D+and+_____________+on+%28a%2Cb%29%2C+then+there+is+at+least+one+c+between+a+and+b+such+that%3A.jpg "Mean Value Theorem If f is ______________ on [a,b] and _____________ on (a,b), then there is at least one c between a and b such that:")
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Example 1: a)Find the c value given in the MVT and b) what does this mean?
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Example 2: Where is the function increasing & decreasing?
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Corollaries
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Vocab/Formulas Antiderivative/Integral: The original function of the derivative Antidifferentiation/Integration
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Example 3: a)Find all possible functions f with the given derivative and b) find the function f that goes through (0,2)
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Example 4: Find the velocity and position of a body falling freely when the acceleration is 9.8 m/sec2 and the body is propelled downward with an initial velocity of 1 m/sec.
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Assignment Pg odd, 43, 51-56
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