The contours of the function f(x, y)= 8x + 4y are all parallel lines with slope 2.

Question

Quizplus · Accepted Answer

The level curves of a function are the curves along which the function takes on a constant value. The slope of a level curve is given by the negative of the gradient of the function at that point. The gradient of the function f(x, y) = 8x + 4y is (8, 4), so the slope of the level curves is -4/8 = -1/2. Therefore, the contours of the function f(x, y) = 8x + 4y are all parallel lines with slope -1/2.

The Contours of the Function F(x, Y)= 8x + 4y