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

[Wi_N]

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?

 

[ehild]

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?

 

[Wi_N]

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.

 

[ehild]

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.

 

[Wi_N]

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.

 

[FactChecker]

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.

 

[ehild]

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

 

[FactChecker]

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.

 

[ehild]

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

 

[FactChecker]

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.