Algorithm to find the maximum/minimum of a polynomial without graphing. For a quadratic equation of the form $y=ax^2+bx+c$ the max/min occurs at $x=-\frac{b}{2a}$. Is there any hard and fast equation like this for polynomials of degree $\geq 4$?. For such polynomials the solution which I got online suggested to plot the curve and find. How to find the absolute maxima without graphing?
If you have a third-degree one, you can derivate your expression (this is quite easy to do by a algorithm of your own, for polynomials). Then you get the max/min by x=-b'/2a'.

For a fourth-degree polynomial, just derivate again, and then use your previous programm for 3rd-deg to find the max/min !

Once you've got an algorithm for degree n, repeat the operation for degree n+1
If you have a third-degree one, you can derivate your expression (this is quite easy to do by a algorithm of your own, for polynomials). Then you get the max/min by x=-b'/2a'.

For a fourth-degree polynomial, just derivate again, and then use your previous programm for 3rd-deg to find the max/min !

Once you've got an algorithm for degree n, repeat the operation for degree n+1