relative/local and absolute/global Maxima and minimas?
i'm so confused and I have a test in two days and idjskladjlks :(
If someone can explain the difference between these two, I would really really really really appreciate it...
thank you so much <3
The local ones are the ones confined to a given domain. I mean the max and min between given x values
The global ones are for the whole graph with no restrictions.
Consider the graph of y=x^2
the global max is infinity and the global min is 0
Now consider the domain \(1\le x\le4\)
For this given domain, the local maximum is 4^2=16 and the local minimum is 1^1=1
Does that make more sense?
thank you so much melody! <3
i'm still sort of confused :')
so let me ask you this....
how do you know if its global? i've heard somethings about the neighborhood around the point and there being other lines around it or something like that but im not really sure what that is about?
A global max or min usually refers to an absolute max or min of a function
A local max or min usually occurs on some specified finite interval
Note that these could be the same, in some cases
For instance.....for the function y = x^2, the absolute (or global ) min occurs at x = 0
However.....if we specify the min on the interval from x = -1 to x = 1......we are talking about a local min.....this is still at x = 0.....so the absolute min and local min are the same in this case.....
oh my god
thank you so much
both of you
thank you Melody and thank you so much CPhill! <3 you both are amazing omg thank you so much
so to clarify,,,
when they don't mention a specific interval its global or absolute but when they do it's local or relative?
Yes that sounds resonable but of course sometimes an interval will include the absolute/global max (or min) and if that is the case then the local max (or min) is also the global one.
That sounds a bit like you are looking at the gradient of the curve at a specific point but that has little to do with global/local minimum/maximum.
If you know enough about the shapes of graphs (or you know some calculus) then you can often know if a point is really a global maximum or minimum. Otherwise you can only know it is a local one.