Answer: C

Expression= 2 (x^2) + 3 (y^2) - 4x - 12y + 18

For extreme values of expression, d/dx(expression) =0

Differentiating with respect to x,

d/dx(expression) = 4x - 4= 0

Therefore, x= 1

Differentiating with respect to y,

d/dy(expression) = 6y - 12= 0

Therefore, y= 2

Substituting values x=1, y=2 in expression,

we get value = 4

It can be ascertained that this extreme value is minimum as d^2/dx^2(expression) = 4 (positive) and d^2/dy^2(expression) = 6 (positive)

Note: Differentiation is not tested on the GMAT, but following little information helps

1. d/dx(constant) = 0

2. d/dx(x^n) = n * x^(n-1)

3. d/dx(c*x) = c ; where c = constant

4. Expression has extreme values at d/dx(expression)=0

; d2/dx^2(expression) = positive signifies minimum value

; d2/dx^2(expression) = negative signifies maximum value

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