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Math Help - Estimating local maxima and minima and identifying multiplicity of factors. #2

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    Estimating local maxima and minima and identifying multiplicity of factors. #2

    estimate the local maxima and minima and identify the mulltiplicity of the factors
    1) F(X)=(2X^2+2X-4)(X^2-6X+9)
    Last edited by mr fantastic; January 23rd 2010 at 02:16 AM. Reason: Changed post title
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    Quote Originally Posted by mamilah View Post
    estimate the local maxima and minima and identify the mulltiplicity of the factors
    1) F(X)=(2X^2+2X-4)(X^2-6X+9)
    You can start by factoring: F(X)= 2(X^2+ X- 2)(X- 3)^2= 2(X+ 2)(X-1)(X- 3)^2. You now know that F has zeros at x= -2, x= 1 and x= 3. Where there is a single zero, the sign changes and F(0)= (-4)(9)< 0. 0 is between -2 and 1 so F is positive for x< -2, negative between -2 and 1, negative again between 1 and 3 and still negative (because -3 is a double root) for x> 3. That indicates that there is a miminum between -2 and 1 and a maximum between 1 and 3. Since the problem only says "estimate", you can use the fact that maxima and minima tend to be halfway between zeros of polynomials.
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