Let f: ℝ2 → ℝ be a twice continuously differentiable non-zero function such that f(t x1, t x2) = t3 f(x1, x2) for all t > 0 and (x1, x2) ∞ ℝ2. Which of the following statements is necessarily true?

For a twice continuously differentiable function Z = f(x, y), a critical point is a saddle point if the Hessian determinant condition satisfies:

Let a, b be distinct positive real numbers. Consider the function f : &mathbb;R2 → &mathbb;R given by f(x, y) = (ax+by)2ax2+by2 for (x, y) ≠ (0, 0) and f(0, 0) = 0. Which of the following statements is true?