I've a problem and I can't find the answer anywhere. Let we say, that we've some defined interval [ x

_{a}, x

_{b}] in which values of a function

*f(x)*must be less than

*y*(

_{max}*f(x) < y*) - this are the design criterias. Now the point is, that I want to use any polynomial or rational function to met such assumption. So e.g. practical case: I want to use such a function

_{max}*f(x)=ax*in situation, where in range [0, 10], values of function are less than -20, and beyond this interval - values should be greater. How can I calculate values of a,b,c,d parameters ?

^{4}+b^{2}x^{3}+cx+dBest Regards,

E.