Thread: 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?

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.

omg im sorry. lol the second one

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.

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?

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.