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Suppose I have a function:
$$f(a,b)=h(a)+g(b)$$
where $a+b=1$. I'm interested in the values of $a$ and $b$ that maximize $f(a,b)$.
Without substitution (e.g. by using the fact that $b=1-a$), how could I find out whether $f(a,b)$ is increasing in $a$?
My approach is as follows: since an incr...
