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baldymcgee6

  • 3 years ago

What two graphical features may occur at a critical value that does not generate a maximum or a minimum?

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  1. ladspeal2
    • 3 years ago
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    horizontal and vertical asymptotes

  2. baldymcgee6
    • 3 years ago
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    nope

  3. baldymcgee6
    • 3 years ago
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    @zepdrix

  4. jim_thompson5910
    • 3 years ago
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    you're thinking of a saddle point maybe http://en.wikipedia.org/wiki/Saddle_point

  5. baldymcgee6
    • 3 years ago
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    the answer is a sharp corner or an inflection point. Such a general question, I think it's just for single variable

  6. jim_thompson5910
    • 3 years ago
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    true, that's another name for it saddle points apply to 1 variable functions as well

  7. baldymcgee6
    • 3 years ago
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    What is a "sharp corner" is that like a cusp?

  8. jim_thompson5910
    • 3 years ago
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    yes

  9. jim_thompson5910
    • 3 years ago
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    something like this |dw:1353381760893:dw|

  10. baldymcgee6
    • 3 years ago
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    same same? Could it not be a vertical asymptote as well? Or what about a single point hole?

  11. jim_thompson5910
    • 3 years ago
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    well here's another example of a sharp point |dw:1353381837898:dw|

  12. jim_thompson5910
    • 3 years ago
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    aka, the absolute value function

  13. baldymcgee6
    • 3 years ago
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    hmmm... interesting.

  14. jim_thompson5910
    • 3 years ago
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    a sharp point is basically a point that is non-differentiable, but the function is still continuous

  15. jim_thompson5910
    • 3 years ago
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    well that's part of the definition anyway

  16. baldymcgee6
    • 3 years ago
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    So why does it show up as a critical value?

  17. jim_thompson5910
    • 3 years ago
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    well if there's a horizontal tangent at this sharp point or saddle point, then the derivative function will have a zero at that point

  18. jim_thompson5910
    • 3 years ago
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    so if you look at the derivative alone, you'll see more critical points than extrema

  19. baldymcgee6
    • 3 years ago
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    If a cusp is non-differentiable are we able to still put a tangent line there?

  20. jim_thompson5910
    • 3 years ago
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    not sure what you mean

  21. baldymcgee6
    • 3 years ago
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    You said at the sharp point it is continuous but not differentiable. I thought we had to be able to differentiate it to have a slope of 0 there?

  22. jim_thompson5910
    • 3 years ago
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    true, now I'm not sure, maybe there are some other criteria for a point to be considered a critical point

  23. baldymcgee6
    • 3 years ago
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    |dw:1353382502904:dw||dw:1353382579141:dw|This produces a local minimum at (0,0), so in this case, the cusp produced a minimum.

  24. jim_thompson5910
    • 3 years ago
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    so maybe a cusp/sharp point isn't a point in which is a critical point, but not an extrema

  25. baldymcgee6
    • 3 years ago
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    Who knows, I'm going to try and find some solid definitions.

  26. jim_thompson5910
    • 3 years ago
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    alright

  27. baldymcgee6
    • 3 years ago
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    thanks for the input.

  28. jim_thompson5910
    • 3 years ago
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    np

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