function behavior

**live_laugh_luv27** · August 9th 2009, 05:02 PM

Which of the following describes the behavior of the graph
$y=\sqrt[4]{|x-2|}$ at $x=2$ ?

1. differentiable
2. corner
3. cusp
4. vertical tangent
5. discontinuity

I think its a cusp..but not sure.
Thanks!

**mr fantastic** · August 9th 2009, 07:54 PM

Originally Posted by live_laugh_luv27

Which of the following describes the behavior of the graph
$y=\sqrt[4]{|x-2|}$ at $x=2$ ?

1. differentiable
2. corner
3. cusp
4. vertical tangent
5. discontinuity

I think its a cusp..but not sure.
Thanks!

Cusp.

Since the tangent does not exist at x = 2 but the curve is continuous, only options 2 and 3 are candidates. But if you look at the definition of each, the answer has to be cusp.

**CaptainBlack** · August 9th 2009, 08:06 PM

Originally Posted by live_laugh_luv27

Which of the following describes the behavior of the graph
$y=\sqrt[4]{|x-2|}$ at $x=2$ ?

1. differentiable
2. corner
3. cusp
4. vertical tangent
5. discontinuity

I think its a cusp..but not sure.
Thanks!

The left and right derivatives go to $\mp$ infinity as $x$ goes to $2$ , which in the case of slopes are the same thing (the curve is vertical on both sides at $x=1$ ) which of course makes the point a cusp.

CB

**mr fantastic** · August 10th 2009, 01:46 AM

Originally Posted by CaptainBlack

The left and right derivatives go to infinity as x goes to 2.

CB

Indeed. Left hand limit $\rightarrow - \infty$ and right hand limit $\rightarrow + \infty$ .

Thread: function behavior

LinkBack

Thread Tools

Display

function behavior

Similar Math Help Forum Discussions

Determine the end behavior of each function...?

Simple basic function end behavior model

Exponential function with espected behavior - removal experiment in ecology

[SOLVED] End Behavior of a function

behavior of a function

Search Tags