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    langebaby's Avatar
    langebaby Posts: 2, Reputation: 1
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    #1

    Oct 15, 2007, 08:14 AM
    college algebra
    if the graph of a polynomial has 3 local minimuns and 3 local maximums, then the equation must be at least to what power?
    langebaby's Avatar
    langebaby Posts: 2, Reputation: 1
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    #2

    Oct 15, 2007, 08:14 AM
    Quote Originally Posted by langebaby
    if the graph of a polynomial has 3 local minimuns and 3 local maximums, then the equation must be at least to what power?
    if the graph of a polynomial has 3 local minimuns and 3 local maximums, then the equation must be at least to what power?
    Gernald's Avatar
    Gernald Posts: 901, Reputation: 93
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    #3

    Oct 15, 2007, 08:23 AM
    Is it the third power?? --don't quote me on that.
    Do you know the equation? If you know that the degree is x to the largest power, the power being the degree.
    Oh I hate math!!
    asterisk_man's Avatar
    asterisk_man Posts: 476, Reputation: 32
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    #4

    Oct 15, 2007, 10:33 AM
    1st power (a line) has 0 max and min
    2nd power (parabola) has 1 max or min
    3rd power has 2 max or min
    4th power has 3 max or min
    terryg752's Avatar
    terryg752 Posts: 197, Reputation: 4
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    #5

    Oct 15, 2007, 06:02 PM
    Let us suppose the polynomial is f(x)

    There are 6 stationary points (Maximum/Minimum points)

    Hence the equation : derivative of f(x) = 0 : must have at least 6 real roots

    Hence derivative of f(x) must be of at least 6 degrees

    Hence f(x) must be of at least 7 degrees

    Hence, Power = at least 7
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