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Math Help - curves

  1. #1
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    Exclamation curves

    "some curves y=x^a has a cusp at x=0, a sharp point like the spine on a holly leaf.

    give three examples of curves which have this property

    If function y=x^a has a cusp, what can you say about y=x^(a)+x,x^(a)+2"

    if anyone understands this question, can you please explain it to me?
    Last edited by scuzi; August 23rd 2008 at 07:41 PM.
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  2. #2
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    First, you are going to have to communicate better.

    In particular, what does this mean: y=x^a+x

    Is that x^{a+x} or x^{a}+x? The latter would be assumed under normal rules.
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  3. #3
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    sorry.

    omg im sorry. lol the second one
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  4. #4
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    okay, i have found that a=2/3, a=4/5 and a=6/7 all have a cusp at x=0. im still not sure what is ment by the second part of the question.
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  5. #5
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    Quote Originally Posted by scuzi View Post
    "some curves y=x^a has a cusp at x=0, a sharp point like the spine on a holly leaf.

    give three examples of curves which have this property

    If function y=x^a has a cusp, what can you say about y=x^(a)+x,x^(a)+2"

    if anyone understands this question, can you please explain it to me?
    The y = (x^a) +x
    and the y = (x^a) +2
    are just vertical translations of the basic y = x^a

    Their graphs are almost the same except that
    >>>that of the y = (x^a) +x is x higher, or x lower, than that of the y = x^a.
    >>>that of the y = (x^a) +2 is always 2 units higher than that of y = x^a.
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