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anonymous
 5 years ago
I don't understand how to find the absolute extrema on an open interval.
anonymous
 5 years ago
I don't understand how to find the absolute extrema on an open interval.

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For example, if the domain is on the interval negative infinity to positive infinity. Not a closed interval.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well, that interval is not closed...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i understand that intuition may tell you that it is

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = 4x^3 3x^4 on the interval negative infintiy to positive infinity

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that is easier to approach

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first note that \[\lim_{x\rightarrow \infty}f(x)=\lim_{x\rightarrow \infty}f(x)=\infty\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you see that? or should we discuss it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0My prof. taught us to find the derivative and at the critical points, weshould look how thederivative behaves, but that doesn't always work..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, but we are doing some preliminary investigation about the behavior of this function

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my point is, this function will have an absolute max because of the result of those limits

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh, can you please explain that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the give f(x) is a polynomial, yes?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so its end behavior will be the same at \[\pm\infty\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, I understand that

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0in this case since the leading coefficient is (1), both ends go to \[\infty\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay so whatever this function does, it can not have an "absolute" minimum right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no, it's suppose to only have an absolute max

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, find the critical points

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i.e. where \[\frac{df}{dx}=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, I understood we always look at the leading coefficient of the polynomial?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes, it as well as the degree will tell you a lot

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you so much! Just one last question..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what level of calculus are you studying and what are your future plans in math?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is calc 1 and the onlysemester of calc i have to take.. thankfully! I'm a pharmacy major..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good luck then, i have had many students that were prepharm

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you. One last question, if the equation was f(x) = 2x^3  6x +2.. the polynomial is of degree 3 and leading coef is positive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so the behavior of function: from negative infinty to positive infinity..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and the critical points are 1 and 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but the solution says there is no extrema and I don'tunderstand why

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, so it will have no "absolute" extrema

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No I can't seem tosee it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its all in that one word "absolute", absolute extreme , implies that the function achieves no values greater/less than, respectively, that value

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if your function runs off to \[+\infty\] one way and \[\infty\] the other, then there is no absolute max/min

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There are however possible "local" max/min which is where many students get confused

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh okay, I will look into it more... Thank you so much foryour help! I really appreciate it!
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