Discussion
Euler's theorem on homogeneous functions states that for a function homogeneous of degree n,
Answer: B
Homogeneity means \( f(tx, ty) = t^{n} f(x,y) \). Differentiating with respect to \( t \) and then setting \( t = 1 \) gives
\[ x f_{x} + y f_{y} \;=\; n f. \]
The weighting by \( x \) and \( y \) is essential: without it the left side is not even of the same degree as the right
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