?Explain why, if f is continuous over [a, b] and is not equal to a constant, there is at

Chapter 5, Problem 201

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Explain why, if f is continuous over [a, b] and is not equal to a constant, there is at least one point \(M \in[a, b]\) such that \(f(M)=\frac{1}{b-a} \int_{a}^{b} f(t) d t\) and at least one point \(m \in[a, b]\) such that \(f(m)<\frac{1}{b-a} \int_{a}^{b} f(t) d t\).

Text Transcription:

M in[a, b]

f(M)=1/b-a int_a^b f(t) dt

m in[a, b]

f(m)<1/b-a int_a^b f(t) dt

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