I've a problem with calculation procedure for parameters of a polynomial. Let we say, that we've defined range $[x_{a}, x_{b}]$ in which values of function $ f(x)$ is less that $y_{max}$. As a $f(x)$ function I treat any polynomial or rational function constructed from parameters $a, b, c, d$ e.g. $f(x)=a \cdot x^4+b \cdot x^2 - \frac{1}{c} \cdot x+d$. Now, I want to calculate such parameters (a, b, c, d) for which mentioned assumption is met - $f(x) < y_{max}$ for $[x_{a}, x_{b}]$. Could you please tell me, how can I resolve such problem ?
Regards, E.