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baldymcgee6
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What two graphical features may occur at a critical value that does not generate a maximum or a minimum?
 2 years ago
 2 years ago
baldymcgee6 Group Title
What two graphical features may occur at a critical value that does not generate a maximum or a minimum?
 2 years ago
 2 years ago

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ladspeal2 Group TitleBest ResponseYou've already chosen the best response.0
horizontal and vertical asymptotes
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
@zepdrix
 2 years ago

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

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
the answer is a sharp corner or an inflection point. Such a general question, I think it's just for single variable
 2 years ago

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

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
What is a "sharp corner" is that like a cusp?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
yes
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
something like this dw:1353381760893:dw
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
same same? Could it not be a vertical asymptote as well? Or what about a single point hole?
 2 years ago

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

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
aka, the absolute value function
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
hmmm... interesting.
 2 years ago

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

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

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
So why does it show up as a critical value?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

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

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
If a cusp is nondifferentiable are we able to still put a tangent line there?
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
not sure what you mean
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
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?
 2 years ago

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

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
dw:1353382502904:dwdw:1353382579141:dwThis produces a local minimum at (0,0), so in this case, the cusp produced a minimum.
 2 years ago

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

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
Who knows, I'm going to try and find some solid definitions.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
alright
 2 years ago

baldymcgee6 Group TitleBest ResponseYou've already chosen the best response.0
thanks for the input.
 2 years ago

jim_thompson5910 Group TitleBest ResponseYou've already chosen the best response.1
np
 2 years ago
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