Level curves and critical points | MIT 18.02SC Multivariable Calculus, Fall 2010
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- Опубликовано: 25 авг 2024
- Level curves and critical points
Instructor: David Jordan
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License: Creative Commons BY-NC-SA
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@Dragonmati
I totally agree.
The only way I think that this would work with having THE SAME contour lines would be to have one global maximum and one local minimum (or vice versa).That could happen by having the first graph with two maximums and just having one of two peaks ''crushed'' inside.
@angel13061987 I agree. If B were a global maximum and C a global minimum, at least the second level (from the outside) would have to pass through the saddle point A, which would result in more of a figure-8 than a squished oval. There is no way for one set of concentric rings to be fully above the second level and the other fully below without crossing through the second level at a "saddle" point (more like a point of inflection in that case).
I beleive that in this specific case, B and C can't be max and min at the same time because there are two cantor lines that have the same figures (the sideways 8 like ones). If B were a minimal and C a max. then the cantor plot would only have one 8 figure and cocentric circles on B and C.
I think you can but not how he showed. Second outer ring could be up...then left two inner go down and right two go up. Hi answer twists the second outer ring...
I think TA made a mistake when drawing the case of one max and one min. If you look at the contour graph, you can see several big loops surrounding the two circles. So that means the dip and the peak have to be located on a basin or a plateau instead of a flat plane z=0.
In the 2nd case A isnt a saddle point.
You're the best, thank you!
But they already told that there is a saddle point ,so C and B must be both minimum or maximum.
yes, that was a mistake.
how would you draw the level curves for the function z=x^3+6xy+3y^2+9x and know how much they are spaced (the level curves)?
Very helpful video, thanks David (My name is also David), wut wutttt
Can you comment Dragonmati comment. I agree with him.