4.2 The Mean Value Theorem State Standard

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Presentation transcript:

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.

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.

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:

Example 1

Example 2

Example 3

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

Example 1

Example 2

Example 3

4.2 Assignemnt Pg. 295 11 – 14 and 1 – 4 (solve using the MVT)