Suppose I have $f(x)A+g(x)B+h(x)C \ge 0$. Here $A,B,C$ can be positive or negative and $f,g,h$ are nonnegative. I would like to obtain a condition for $f,g,$ and $h$ such that $f'(x)A+g'(x)B+h'(x)C \ge 0$. I will appreciate any substantial comments.
Conditions for some inequality
0
$\begingroup$
inequality
-
1Unless you tell us more about $f$, $g$, $h$ and the $x$-domain $I$ where all this should hold the condition $f'(x)A+g'(x)B+h'(x)C \ge 0$ cannot be transformed into something simpler. If $I$ is a compact interval then the assumption $f(x)A+g(x)B+h(x)C \ge 0$ is useless, because by adding a suitable constant to $f$ you always can force it to hold without changing the derivative(s). – 2011-07-09
-
0$I$ is a compact interval, and $A, B, C $are given. – 2011-07-09