How do I do the mean value theorem in this equation. f(x) = x^2+2x-1 , [0,1]

Question

mathmale · Answer

Understanding the "mean value theorem" would help.  What, specifically, does this theorem say?  Any questions about it?

mathmale · Answer

The mean value theorem involves 2 different slope calculations:  one is to take the derivative of the given function; the other is to find the average value of the function on the given interval.

aries94 · Answer

The questions says to find the value or values of c that satisfy equation (1) in the conclusion of the mean value theorem for the function and interval.

mathmale · Answer

Exactly.  So please tell me more about what you have learned about applying the mean value theorem.  Supposing the conditions of the theorem are satisfied, what would a positive statement of the expected outcome be?  You have to understand the purpose of the theorem before applying it makes any sense.

mathmale · Answer

It'd make a lot more sense to you as well as to me if you'd look up the mean value theorem , explain the conditions and the conclusion.    Right now it appears you're wandering around in the dark.

mathmale · Answer

What are the conditions that must be met before you can apply the MVT?
What is the conclusion you can make?  You need to be able to explain this conclusion in words.

mathmale · Answer

Have you looked up "MVT" yet?

aries94 · Answer

yeah I saw a website that It states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b)

mathmale · Answer

Yes, and what makes up the equation you are showing is true?

Hint:  Both are SLOPES.  One is calculated by finding the derivative of the function f(x), the other is calc. by using the "average value of a function on a given interval" equation.  You MUST understand both before this question will make any sense to you.

mww · Answer

There is a neat graphical and formulaic representation.

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Algebraically
$$\frac{ f(b) - f(a) }{ b-a } = f'(c) ~ for~some~c~\in~(a,b)$$
f must be continuous over [a,b] and differentiable over (a,b)