I'm looking for a local minimum point that doesn't show up when....

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Wi_N
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Homework Statement


I set the derivative to 0. i get 1 real root a max point and 2 imaginary. How can i find that local min?

what techniques are available?
 
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Wi_N said:

Homework Statement


I set the derivative to 0. i get 1 real root a max point and 2 imaginary. How can i find that local min?

what techniques are available?
How do you know that the critical point is maximum? What is the function you want to find the local minimum of?
 
ehild said:
How do you know that the critical point is maximum? What is the function you want to find the local minimum of?

i plotted the graph. there is a min point and a max point. but only the max point is attainable through der=0

arctanx -ln(x)/6 - x/3

max point at x=1 but the min x=0.28 can't be found using der.
 
Wi_N said:
i plotted the graph. there is a min point and a max point. but only the max point is attainable through der=0

arctanx -ln(x)/6 - x/3

max point at x=1 but the min x=0.28 can't be found using der.
How did you get the other roots? Show your work.
 
ehild said:
How did you get the other roots? Show your work.

thank you for your help. i must be going crazy or blind but i solved it.
 
Please use parentheses in your equations to make them clear. They do not cost anything. ;>)

Note: Since arctan is a strictly increasing function, you might get a simpler problem by ignoring the arctan. It depends on whether the problem is ##atan( -ln(x)/6 - x/3 )## or ##atan( -ln(x)/6 ) - x/3 ##.

CORRECTION: I see that the function is atan(x)-ln(x)/6-x/3. Maybe that should have been obvious to me.
 
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Wi_N said:
thank you for your help. i must be going crazy or blind but i solved it.
It would be useful for other people if you showed the way of solution
 
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If there is only one real zero of the derivative (as stated in post #1), there can not be a local max and a local min (as stated in post #3). Complex derivative zeros will not add a local extreme point on the real line.
 
FactChecker said:
If there is only one real zero of the derivative (as stated in post #1), there can not be a local max and a local min (as stated in post #3). Complex derivative zeros will not add a local extreme point on the real line.
There are three real zeros of the derivative, but one is at negative x where the function is not defined. The OP made some mistake, and he found it an got the minimum, see Post #5
 
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ehild said:
There are three real zeros of the derivative, but one is at negative x where the function is not defined. The OP made some mistake, and he found it an got the minimum, see Post #5
Right. I just wanted to point out that there was a mistake that was clear just from basic principles.