Question

When does a parametric curve have spikes or cusps?

Answer 1

@TuringTest

Answer 2

@KingGeorge

Answer 3

you would have to find where ther derivative\[\frac{dy}{dx}\]is not conitnuous

Answer 4

So I would take the derivative of y then put it over the the derivative of x?

Answer 5

for a parametric curve\[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dy}{dt}}\]yep, what you just said

Answer 6

So it would be 3x^2-2 / 2/x -2

Answer 7

3x^2-3 on top actually

Answer 8

if I'm imagining parentheses in the right places then yes

Answer 9

Sorry about that. (3x^2-3)/ ((2/x) -2)
How would you know when it is not continuous

Answer 10

when it's undefined

Answer 11

So that would mean it was at t =1 and t=0?

Answer 12

wait a darn minute, you have x(t) defined in terms of x
that is a typo I take it, those should be t's, right?

Answer 13

Yeah

Answer 14

so yeah, t=0 and t=1 look to be the likely culprits
not sure how to go deeper into proving it, but you are only asked for points that "might" be spiky, so hopefully that's enough

Answer 15

Alright thanks.

Answer 16

welcome!