Math Is Fun Forum

Prakash Panneer

Member

Registered: 2006-06-01

Posts: 110

Is this right or wrong?

An example of a function on a closed interval which satisfies a conclusion of the mean value theorem, but not the hypothesis.

f(x) = (1/2)x^2    x =3
           4               x = 3 in a closed interval [2,4]

Please help me.

Thanks in advance

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Letter, number, arts and science
of living kinds, both are the eyes.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Is this right or wrong?

Didn't we just have this question?  In any case, if you meant:

f(x) = (1/2)x^2    x !=3 (does not equal 3)
           4               x = 3 in a closed interval [2,4]

Then yes, that function does not satisfy the hypothesis, but does so for the conclusion.

Edit: Upon further review, this is the third post you have made, Prakash, on this same exact question.  Please, keep all posts about the same question inside the same topic.  If you feel you haven't gotten an answer, you should bump your topic instead.  "Bump" simply means make a little post in it saying "I need help still" and that will move your topic to the top of the message board.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."