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- anonymous

Does a differentiable function have to have a relative minimum between any two relative maxima? Why?

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- anonymous

Does a differentiable function have to have a relative minimum between any two relative maxima? Why?

- schrodinger

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- Hero

Because otherwise, it wouldn't be a function? |dw:1328463326481:dw|

- anonymous

yup i concur with hero

- Hero

Without a relative min, if you wanted to create a function between two points, it would essentially be a line. A line doesn't have a relative min/max.

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- anonymous

Thank you! I can't think of another counterexample. Is a line a counterexample, though?

- anonymous

well as a matter of fact it would be..as it would not be havin rel. maximas/minimas

- anonymous

What I don't understand is this: How can a line disprove the statement if that line does not have the two maxima in the first place?

- anonymous

According to my class, it must have minimum. That was the correct answer. Thank you both very much.

- anonymous

all the credit goes to hero...

- Hero

The line is there to show you that if you drew the line to create a function, you would have a function, but you wouldn't have a minimum, maximum or any of the such.

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