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?

Simple logic- in the real numbers, your function is always negative, since powers of e are positive. Thus you want to minimise the magnitude of your function to maximise it. To do this, you want as small a power as possible. Thus you need to maximise the second function, as this will produce the smallest power for e possible. Make sense?

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