Finding the local minimum of a graph

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Homework Help Overview

The discussion revolves around identifying local minimums on a provided graph, with specific values being debated. The original poster expresses confusion regarding the identification of local minimums, particularly questioning the inclusion of x=1 as a local minimum according to the answer key.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of a local minimum and question the conditions under which a point can be classified as such. The original poster attempts to reconcile their findings with the answer key, while others prompt them to consider the values of y near the points in question.

Discussion Status

The conversation is ongoing, with participants providing insights into the definition of local minimums and discussing specific points on the graph. There is a productive exchange of ideas, particularly regarding the nature of local minimums and maximums, though no consensus has been reached on the specific values.

Contextual Notes

Participants are working with a graph that is not continuous, which raises questions about the applicability of the local minimum definition in this context. The original poster's confusion stems from differing interpretations of the answer key and the graph's characteristics.

JustinLiang
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Homework Statement


The question provides a graph and asks for the local minimums. I attached a picture with the graph.

2. The attempt at a solution
I said the local minima are when x=0,2,5.

However the answer key suggests they are at 1,2,5.
Could someone please explain why 1 is a local minimum? It is just a point on the graph...
Maybe the answer key is wrong.
 

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Recall how "local minimum" is defined.

ehild
 
ehild said:
Recall how "local minimum" is defined.

ehild

So local minimum tells us that a y value near the point is always greater than the y value of the point. That is why we can call it the local minimum. However, in this case the dot is no continuous, so there is no y value near it to compare?

I understand why 0 cannot be a local minimum but I fail see see why 1 can be.
 
Are the y(x) values near to x=1 higher than y(1)? The function does not need to be continuous to have a local minimum. ehild
 
ehild said:
Are the y(x) values near to x=1 higher than y(1)? The function does not need to be continuous to have a local minimum.


ehild

Ah okay, but what about x=6? Values near it are both lower, isn't that a local minimum then?
 
If all values near x=6 are lower than y(6) so y(6) is higher then anything else nearby, is it a minimum?

ehild
 
JustinLiang said:
Ah okay, but what about x=6? Values near it are both lower, isn't that a local minimum then?
No, its a local maximum!
 
HallsofIvi,

I know that you know it, (and I hope you think that I also know it) but I asked the OP...:wink:


ehild
 

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