Finding local and absolute maxima values of a polynomial

I have a polynomial of 3.3x^6 - 23.63x^5 + 65.18x^4 - 86.97x^3 + 56x^2 - 15.4x + 1.41; I am trying to solve for the local maxima (preferably absolute maxima) for this equation. I need both x and y values for the maxima. Please let me know the best way to do this for a series of 10 polynomials

Thanks,

Answer 1

[Walter Roberson]

The typical calculus method is to differentiate and solve for the differentiated function equal to 0. That gives you all of the minima, maxima, and saddle points. You then differentiate the function again and evaluate at the roots you found a moment before, and the places the value is negative correspond to maxima. Select for those, take the corresponding x values back to the original equation, evaluate, pick out the largest to get the global maxima.

Hint: since you have numeric coefficients, you can do a numeric differentiation and use roots(). You will need to think a brief moment about how the coefficients that have to be passed to roots() relate to your original coefficients.