How do I find the extrema of the function x^3+6 x^2-13 x-42?

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Pedro 2012-9-10

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In the optimizing section there is function that calculates minima but not all the extrema. And how to I do for the multiple variable functions, like, (-x-2)^2+(-y-3)^2?

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Pedro 2012-9-10

I guess I messed up there, I actually want to know the method for both types of functions.

Rick Rosson 2012-9-10

Please post two separate questions.

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Walter Roberson 2012-9-10

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For polynomials, the extrema are always one of the infinities.

Take the highest order term. If it is an even power, then both extrema have the same sign, which will be the same as the sign of that highest-order term. If the highest order term is an odd power, then the extrema have opposite signs, with the limit towards +infinity having the same sign as the highest-order term, and the limit towards -infinity having the opposite sign as the highest-order term.

If you want to find all the minima and all the maxima, and you have a routine to find minima, then use it once to find the minima, and then feed in the negative of the expression and find the minima of that and invert their signs to get the maxima.