ABSOLUTE MAX AND ABSOLUTE MIN

Creasion

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Sep 10, 2019
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Yea, this assignment has got me stumped.

More at the absolute minimum part, would it be the y = infinity or what?

And can the local minimum and absolute minimum be the same?
as in can the sets coincide?

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Dr.Peterson

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Nov 12, 2017
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The absolute maximum is commonly one of the relative maxima; these are not disjoint sets.

The absolute minimum or maximum does not have to exist (note the comment, "if they exist"). If you want to say one of them is infinity (or negative infinity), you are probably seeing that it doesn't exist.

Now solve it, and eat that cookie!
 

pka

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Jan 29, 2005
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8,527
Yea, this assignment has got me stumped.

More at the absolute minimum part, would it be the y = infinity or what?

And can the local minimum and absolute minimum be the same?
as in can the sets coincide?

View attachment 13555

WHOEVER CAN SOLVE IT I'LL GIVE YOU A COOKIE!!
You supply the values of \(\displaystyle \Large{\bf ?}\)
Local max \(\displaystyle (-3,?)~\&~(?.3)\)
Abs Max \(\displaystyle (?,4)\)

Local Min: \(\displaystyle (?,0)~\&~(3,?)\)
Abs Min \(\displaystyle (?,?)\).
 

Otis

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Apr 22, 2015
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… at the absolute minimum part, would it be … infinity …?
I'm guessing that you meant to write 'maximum' or else 'negative infinity'. Either way, the answer is no. If any type of minimum or maximum exists, it is always a Real number. In cases where there's no answer, it's somewhat standard to report 'DNE' (does not exist).

And can the local minimum and absolute minimum be the same?
Not in this exercise, but with other functions it is possible. In this exercise, you can see that the local maximum between x=-1 and x=1 is also the absolute maximum.

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