Teaching CSIR NET Mock Test Series Mathematical Science Analysis Directional Derivative, Partial Derivative
Let f : ℝ2 → ℝ3 be a differentiable function such that (Df)(0, 0) has rank 2 Writhe f = (f1, f2, f3). Which of the following statements are necessarily true?
1
f is injective in a neighbourhood of (0, 0)
2
There exists an open neighbourhood U of (0, 0) in ℝ2 such that f3 is a function of f1 and f2
3
f maps an open neighbourhood of (0, 0) in ℝ2 onto an open subset of ℝ3
4
(0, 0) is an isolated point of f-1 ({f(0, 0)})