## An increasing implicit function

For the relation $$x^2 + 2xy^2 + y^4 - y^5 = 0$$. Prove following.
This relation defines a smooth function $$y = f(x)$$ in some neighborhood of the point $$0$$, for which $$f(0) = 1$$ holds.
The function $$f$$ is increasing in some neighborhood of the point $$0$$.