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anonymous

  • 4 years ago

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

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  1. Hero
    • 4 years ago
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    Because otherwise, it wouldn't be a function? |dw:1328463326481:dw|

  2. anonymous
    • 4 years ago
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    yup i concur with hero

  3. Hero
    • 4 years ago
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    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.

  4. anonymous
    • 4 years ago
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    Thank you! I can't think of another counterexample. Is a line a counterexample, though?

  5. anonymous
    • 4 years ago
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    well as a matter of fact it would be..as it would not be havin rel. maximas/minimas

  6. anonymous
    • 4 years ago
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    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?

  7. anonymous
    • 4 years ago
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    According to my class, it must have minimum. That was the correct answer. Thank you both very much.

  8. anonymous
    • 4 years ago
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    all the credit goes to hero...

  9. Hero
    • 4 years ago
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    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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