While local max and min are the function values lowest or highest on a specific curve of the graph, the global max and mins are the highest and lowest points of the entire function, respectively. Because those points are the lowest and highest of the entire function, they are more extreme than any points on the same curve as well. Therefore they are also local max and mins, and the lowest local min and highest local max are the global mins and maxs, respectively.
To find the global max and mins you compute all critical points and find the most extreme ones.
Challenges
I understand that the global min would also be the local min. Because all animal are not cats while all cats are animals, then why does the local min have to be a global min. I just realized that its not, but one has to be. The contrapostive is that if its not a local min it's not a global min. So i guess i no longer have a challenge but the whole point of the blog is to teach yourself so i hope that's okay.
Reflections.
It makes sense that the global max and min are important because this can show you how to obtain the greatest yield or minimize damage for a real world problem. Now I don't understand why the local mins and max's are important. Is it just to find to global ones? Perhaps i should switch my challenges and reflections paragraph.
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