Find the absolute minimum value of the function
$$f ( x , y ) = 6 + 3 x y - 2 x - 4 y$$
on the set $D . D$ is the region bounded by the parabola $y = x ^ { 2 }$ and the line $y = 4$
Select the correct answer.
A) $- 31$
B) $- 30$
C) 30
D) $- 32$
E) 0

Question

Quizplus · Accepted Answer

The absolute minimum value occurs at the critical point within the region or on the boundary. Evaluating $f(x, y)$ at the critical point and on the boundary, the minimum value is $-30$.

Find the Absolute Minimum Value of the Function f(x,y)=6+3xy−2x−4yf ( x , y ) = 6 + 3 x y - 2 x - 4 yf(x,y)=6+3xy−2x−4y

Find the Absolute Minimum Value of the Function $f ( x , y ) = 6 + 3 x y - 2 x - 4 y$