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Mean value theorem : explained

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The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any.

10. Find the numbers c referred to in the mean value theorem for integrals for each function, over the interval indicated.

Please see attached.

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Solution Summary

This shows how to find the numbers for the mean value theorem for given functions.

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According to the mean value theorem, there exists a c between a and b such that:

int(f(x), a, b)= (b-a)*f(c)

Note that I have shown the definite integral of f(x) from x=a to x=b by int( f(x), a, b).

(a)
f(x)=6x^2, a=-3, b=4, so the theorem implies that: there exists a c between -3 and 4 such ...

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