How do you know that the critical point is maximum? What is the function you want to find the local minimum of?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?
ehild said:How do you know that the critical point is maximum? What is the function you want to find the local minimum of?
How did you get the other roots? Show your work.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.
ehild said:How did you get the other roots? Show your work.
It would be useful for other people if you showed the way of solutionWi_N said:thank you for your help. i must be going crazy or blind but i solved it.
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 #5FactChecker 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.
Right. I just wanted to point out that there was a mistake that was clear just from basic principles.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
A local minimum point is a point on a graph where the function reaches the lowest value within a specific interval. It is lower than all the other points immediately surrounding it, but it may not be the overall lowest point on the entire graph.
To find a local minimum point, you must first identify the interval where you suspect the local minimum point exists. Then, you can use a variety of methods such as taking the derivative and setting it equal to zero, using the first derivative test, or graphing the function to visually locate the lowest point within the interval.
If a local minimum point does not show up on a graph or in a function, it means that there is no point within the specified interval that is lower than all the other points. This could be due to a variety of reasons, such as the function being constant or the interval being too large.
Yes, a local minimum point can change if the function or the interval is changed. For example, if the function is shifted up or down, the local minimum point will also shift. Similarly, if the interval is expanded or contracted, the local minimum point may also change.
A local minimum point is a point on a graph where the function reaches the lowest value within a specific interval. A global minimum point is the overall lowest point on the entire graph. In other words, a local minimum point is only guaranteed to be the lowest point within a certain interval, while a global minimum point is the lowest point on the entire graph.