Find the absolute maxima and minima of the function on the given domain.
-f(x, y) = 4x + 3y on the trapezoidal region with vertices (0, 0), (1, 0), (0, 2), and (1, 1)
A) Absolute maximum: 6 at (0, 2); absolute minimum: 0 at (0, 0)
B) Absolute maximum: 7 at (1, 1); absolute minimum: 0 at (0, 0)
C) Absolute maximum: 8 at (2, 0); absolute minimum: 4 at (1, 0)
D) Absolute maximum: 7 at (1, 1); absolute minimum: 4 at (1, 0)

Question

Quizplus · Accepted Answer

To find the absolute maxima and minima, evaluate the function at the vertices of the trapezoidal region. For (0, 0), f(0, 0) = 0; for (1, 0), f(1, 0) = 4; for (0, 2), f(0, 2) = 6; for (1, 1), f(1, 1) = 7. Thus, the absolute maximum is 7 at (1, 1) and the absolute minimum is 0 at (0, 0).

Find the Absolute Maxima and Minima of the Function on the Given