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horizontal and vertical asymptotes

nope

you're thinking of a saddle point maybe
http://en.wikipedia.org/wiki/Saddle_point

true, that's another name for it
saddle points apply to 1 variable functions as well

What is a "sharp corner" is that like a cusp?

yes

something like this
|dw:1353381760893:dw|

same same? Could it not be a vertical asymptote as well? Or what about a single point hole?

well here's another example of a sharp point
|dw:1353381837898:dw|

aka, the absolute value function

hmmm... interesting.

a sharp point is basically a point that is non-differentiable, but the function is still continuous

well that's part of the definition anyway

So why does it show up as a critical value?

so if you look at the derivative alone, you'll see more critical points than extrema

If a cusp is non-differentiable are we able to still put a tangent line there?

not sure what you mean

so maybe a cusp/sharp point isn't a point in which is a critical point, but not an extrema

Who knows, I'm going to try and find some solid definitions.

alright

thanks for the input.