Mean Value Theorem


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Hey i got a bastage calculus test today at 5:30, so can anyone tell me how to do this mean value theorem concept?? My teacher didnt do anything but prove it exists, and i have no idea how to actually use it to solve a problem. Thnx.

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Here ya go:

Let f be a function that satisfies the following hypothesis:

1)f is continuous on the closed interval [a,b]

2)f is differentiable on the open interval (a,b)

There there is a number c in (a,b) such that

f '©= ( f(b)-f(a) ) / (b-a)

or

f(b)-f(a)=f '©(b-a)

My "retarded" calculus 12 class is still two chapters behind, we're slow, but this is what I understand from my book.

So this means that Lets say f(b) = 3 and f(a)=5. Let b = 4 and a=2.

f '© = -1.

I guess use it to find the slope at a given point.

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