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anonymous
 3 years ago
What two graphical features may occur at a critical value that does not generate a maximum or a minimum?
anonymous
 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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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0horizontal and vertical asymptotes

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1you're thinking of a saddle point maybe http://en.wikipedia.org/wiki/Saddle_point

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the answer is a sharp corner or an inflection point. Such a general question, I think it's just for single variable

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1true, that's another name for it saddle points apply to 1 variable functions as well

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0What is a "sharp corner" is that like a cusp?

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1something like this dw:1353381760893:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0same same? Could it not be a vertical asymptote as well? Or what about a single point hole?

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1well here's another example of a sharp point dw:1353381837898:dw

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1aka, the absolute value function

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1a sharp point is basically a point that is nondifferentiable, but the function is still continuous

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1well that's part of the definition anyway

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So why does it show up as a critical value?

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1well if there's a horizontal tangent at this sharp point or saddle point, then the derivative function will have a zero at that point

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1so if you look at the derivative alone, you'll see more critical points than extrema

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0If a cusp is nondifferentiable are we able to still put a tangent line there?

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1not sure what you mean

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You 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?

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1true, now I'm not sure, maybe there are some other criteria for a point to be considered a critical point

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1353382502904:dwdw:1353382579141:dwThis produces a local minimum at (0,0), so in this case, the cusp produced a minimum.

jim_thompson5910
 3 years ago
Best ResponseYou've already chosen the best response.1so maybe a cusp/sharp point isn't a point in which is a critical point, but not an extrema

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Who knows, I'm going to try and find some solid definitions.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thanks for the input.
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