# maximize two functions, but have the same optimal solution

by nguyy   Last Updated September 21, 2018 20:20 PM

I have a function, $$-e^{-(x-(1/2)x^2)}$$.

If I'm maximizing the function $$-e^{-(x-(1/2)x^2)}$$ with the respect of X, it would give me the same result (optimal solution of X) as if I was maximizing $$x-(1/2)x^2.$$ Why is that so?

I know that the first order derivatives of both function will be the same. But why?

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