An increasing implicit function
Task number: 3223
For the relation \(x^2 + 2xy^2 + y^4 - y^5 = 0\). Prove following.
Variant 1
This relation defines a smooth function \(y = f(x)\) in some neighborhood of the point \(0\), for which \(f(0) = 1\) holds.
Variant 2
The function \(f\) is increasing in some neighborhood of the point \(0\).
