Increasing in parametrics

Question

Let $C=\{(x(t),y(t)) \mid 0 \leq t \leq 1 \}$ be a curve in $R^2$.

Does it have sense to say that $C$ is increasing/decreasing or what is inreasing/decreasing is the function in implicit that describe $C$.

Is it posible to describe $C$ with two parametrics function and to change the first parametric function into an inceasing function and the second function in a deceasing function?

If C is increasing/decreasing, How can I know with a parametrization of $C$ without changing it to implicit?

Answer 1

Not sure but,

• if $x'(t) \cdot y'(t) >0 $ then $y=f(x)$ is increasing
• if $x'(t) \cdot y'(t) <0 $ then $y=f(x)$ is decreasing

¿correct?