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Math Help - Minimum and Maximum points of polynomials.

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    Senior Member sakonpure6's Avatar
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    Minimum and Maximum points of polynomials.

    When looking at polynomials other than quadratic and linear, assuming we are given a cubic function where it has a maximum in between 2 real roots such as 5 and 4. Can we say that it is a max/minimum at x= (5+4)/2 = 4.5???

    Also at those points, the rate of change is 0 right?
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    Re: Minimum and Maximum points of polynomials.

    Quote Originally Posted by sakonpure6 View Post
    When looking at polynomials other than quadratic and linear, assuming we are given a cubic function where it has a maximum in between 2 real roots such as 5 and 4. Can we say that it is a max/minimum at x= (5+4)/2 = 4.5???

    Also at those points, the rate of change is 0 right?
    No. but if it has only two real roots, that means one of its extrema is tangent to the x-axis. That means, one simple root and one double root, or a root of multiplicity 2
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    Senior Member Paze's Avatar
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    Re: Minimum and Maximum points of polynomials.

    Quote Originally Posted by sakonpure6 View Post
    When looking at polynomials other than quadratic and linear, assuming we are given a cubic function where it has a maximum in between 2 real roots such as 5 and 4. Can we say that it is a max/minimum at x= (5+4)/2 = 4.5???

    Also at those points, the rate of change is 0 right?
    No. Sometimes the point right in between two roots can even be undefined. But you are right that at a minima and maxima, the rate of change is 0.
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    Re: Minimum and Maximum points of polynomials.

    Quote Originally Posted by Paze View Post
    No. Sometimes the point right in between two roots can even be undefined. But you are right that at a minima and maxima, the rate of change is 0.
    Perhaps you mean by "undefined" it is not readily known. You could find it: if x0 = (x1+x2)/2, then f(x0) is known.
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