In this lesson, we will learn how to interpret and use the mean value theorem and Rolle’s theorem.
Q1:
Mason is not convinced that the mean value theorem is true because, he says, the function π(π₯)=|π₯| has the property that if we take π=β2 and π=2, we have π(π)βπ(π)πβπ=0, and yet there is no point π₯ where πβ²(π₯)=0. What is his error?
Q2:
Madison is not convinced that the mean value theorem is true because, she says, the function π(π₯)=|π₯| is certainly differentiable on ββ{0}. But if we take π=β1 and π=1, we have π(π)βπ(π)πβπ=0, and yet there is no point π₯ where πβ²(π₯)=0. What is her error?
Q3:
Does the mean value theorem apply for the function π¦=2βπ₯β4ο¨ over the interval [β2,2]?
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