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

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ladspeal2Best ResponseYou've already chosen the best response.0
horizontal and vertical asymptotes
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
you're thinking of a saddle point maybe http://en.wikipedia.org/wiki/Saddle_point
 one year ago

baldymcgee6Best 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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
true, that's another name for it saddle points apply to 1 variable functions as well
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
What is a "sharp corner" is that like a cusp?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
something like this dw:1353381760893:dw
 one year ago

baldymcgee6Best 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?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
well here's another example of a sharp point dw:1353381837898:dw
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
aka, the absolute value function
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
hmmm... interesting.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
a sharp point is basically a point that is nondifferentiable, but the function is still continuous
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
well that's part of the definition anyway
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
So why does it show up as a critical value?
 one year ago

jim_thompson5910Best 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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
so if you look at the derivative alone, you'll see more critical points than extrema
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
If a cusp is nondifferentiable are we able to still put a tangent line there?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
not sure what you mean
 one year ago

baldymcgee6Best 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?
 one year ago

jim_thompson5910Best 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
 one year ago

baldymcgee6Best 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.
 one year ago

jim_thompson5910Best 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
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
Who knows, I'm going to try and find some solid definitions.
 one year ago

baldymcgee6Best ResponseYou've already chosen the best response.0
thanks for the input.
 one year ago
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