Discussion
The stationary point of \( f(x,y) = x^{2} + y^{2} - 4x - 6y + 20 \) lies at
Answer: C
Set both first derivatives to zero:
\[ f_{x} \;=\; 2x - 4 \;=\; 0, \qquad f_{y} \;=\; 2y - 6 \;=\; 0, \]
giving \( x = 2 \) and \( y = 3 \). Since \( f_{xx} = f_{yy} = 2 \) and \( f_{xy} = 0 \), the discriminant is \( D = 4 > 0 \) with \( f_{xx} > 0 \), so the point is a minimum, of value seven
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