# curves

• Aug 23rd 2008, 06:26 PM
scuzi
curves
"some curves y=x^a has a cusp at x=0, a sharp point like the spine on a holly leaf.

give three examples of curves which have this property

If function y=x^a has a cusp, what can you say about y=x^(a)+x,x^(a)+2"

if anyone understands this question, can you please explain it to me?(Worried)
• Aug 23rd 2008, 06:47 PM
TKHunny
First, you are going to have to communicate better.

In particular, what does this mean: y=x^a+x

Is that \$\displaystyle x^{a+x}\$ or \$\displaystyle x^{a}+x\$? The latter would be assumed under normal rules.
• Aug 23rd 2008, 07:00 PM
scuzi
sorry.
omg im sorry. lol the second one
• Aug 23rd 2008, 11:25 PM
scuzi
okay, i have found that a=2/3, a=4/5 and a=6/7 all have a cusp at x=0. im still not sure what is ment by the second part of the question.
• Aug 24th 2008, 12:17 AM
ticbol
Quote:

Originally Posted by scuzi
"some curves y=x^a has a cusp at x=0, a sharp point like the spine on a holly leaf.

give three examples of curves which have this property

If function y=x^a has a cusp, what can you say about y=x^(a)+x,x^(a)+2"

if anyone understands this question, can you please explain it to me?(Worried)

The y = (x^a) +x
and the y = (x^a) +2
are just vertical translations of the basic y = x^a

Their graphs are almost the same except that
>>>that of the y = (x^a) +x is x higher, or x lower, than that of the y = x^a.
>>>that of the y = (x^a) +2 is always 2 units higher than that of y = x^a.