| Homogeneous function | Degree | ||
| A. | \(f(x,y)=\frac{x^\frac{1}{3}+y^\frac{1}{3}}{x^\frac{1}{2}+y^\frac{1}{2}}\) | I. | 3 |
| B. | \(f(x,y)=\frac{x+y}{\sqrt{x}+\sqrt{y}}\) | II. | \(\frac{1}{2}\) |
| C. | \(f(x,y)=\frac{x^4+y^4}{x+y}\) | III. | 1 |
| D. | \(f(x,y)=\frac{\sqrt{x^3+y^3}}{\sqrt{x}+\sqrt{y}}\) | IV. | \(-\frac{1}{6}\) |
Let \( f : [1, \infty) \to [2, \infty) \) be a differentiable function. If
\( 10 \int_{1}^{x} f(t) \, dt = 5x f(x) - x^5 - 9 \) for all \( x \ge 1 \), then the value of \( f(3) \) is ______.


