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4.2 Notes Rolles and MVT

# 4.2 Notes Rolles and MVT - can be applied find all values...

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Calculus I Section 4.2 – Rolle’s Theorem and the Mean Value Theorem Rolle’s Theorem Let f be a continuous function on the closed interval [ a, b ] and differentiable on the open interval ( a, b ). If f(a)=f(b) then there is at least one number c in ( a, b ) such that 0 ) ( = c f . Hypotheses: ________________________________________________________________ Conclusion: ________________________________________________________________ Diagram illustrating the theorem: Determine whether Rolle’s Theorem can be applied to on the interval [1,3]. If Rolle’s Theorem can be applied, find all values of c guaranteed by the theorem. Determine whether Rolle’s Theorem can be applied to on the interval [0, 2 ]. If Rolle’s Theorem

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Unformatted text preview: can be applied, find all values of c guaranteed by the theorem. The Mean Value Theorem Let f be a continuous function on the closed interval [ a, b ] and differentiable on the open interval ( a, b ), then there is at least one number c in ( a, b ) such that a b a f b f c f--= ′ ) ( ) ( ) ( . Hypotheses: ________________________________________________________________ Conclusion: ________________________________________________________________ Diagram illustrating the theorem: Determine whether the MVT can be applied to each function on the given interval. If so, find the values of c guaranteed by the theorem. 1) over [-1,1] 2) over [-8,8] 3) over...
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4.2 Notes Rolles and MVT - can be applied find all values...

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