Finding the local minimum of a graph

  • #1

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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Answers and Replies

  • #2
ehild
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Recall how "local minimum" is defined.

ehild
 
  • #3
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.
 
  • #4
ehild
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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
 
  • #5
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?
 
  • #6
ehild
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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
 
  • #7
HallsofIvy
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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!
 
  • #8
ehild
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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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