4.2 Mean Value Theorem.

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Presentation transcript:

4.2 Mean Value Theorem

How to differentiate Absolute Value

Max’s, Min’s, Increasing, Decreasing CP y y' x CP y y' Definitions & Corollary 1

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:

Example 1: a)Find the c value given in the MVT and b) what does this mean?

Example 2: Where is the function increasing & decreasing?

Corollaries

Vocab/Formulas Antiderivative/Integral: The original function of the derivative Antidifferentiation/Integration

Example 3: a)Find all possible functions f with the given derivative and b) find the function f that goes through (0,2)

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.

Assignment Pg. 202 1-33 odd, 43, 51-56