Which of the following describes the behavior of the graph

$\displaystyle y=\sqrt[4]{|x-2|}$ at $\displaystyle x=2$?

1. differentiable

2. corner

3. cusp

4. vertical tangent

5. discontinuity

I think its a cusp..but not sure.

Thanks!

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- Aug 9th 2009, 05:02 PMlive_laugh_luv27function behavior
Which of the following describes the behavior of the graph

$\displaystyle y=\sqrt[4]{|x-2|}$ at $\displaystyle x=2$?

1. differentiable

2. corner

3. cusp

4. vertical tangent

5. discontinuity

I think its a cusp..but not sure.

Thanks! - Aug 9th 2009, 07:54 PMmr fantastic
- Aug 9th 2009, 08:06 PMCaptainBlack
The left and right derivatives go to $\displaystyle \mp$ infinity as $\displaystyle x$ goes to $\displaystyle 2$, which in the case of slopes are the same thing (the curve is vertical on both sides at $\displaystyle x=1$) which of course makes the point a cusp.

CB - Aug 10th 2009, 01:46 AMmr fantastic