Algorithm to Change a Function to Meet a Condition on It's Minima

Question

Given a continuous function $f(x)$ ($f$ does not always have to be a polynomial), with $f(x) \geq 0$ for all values of $x$, is there a method to modify $f(x)$ to another continuous function $g(x)$ so that the only minima $b$ of $g(x)$ are those that $f(b)<10$?

Answer 1

In general no. However if the you are able to differentiate the function and find $f'(x) = 0$ you then can find the minima then you can work out if the function goes below $m$.