Question

Find fx(1, 0) and fy(1, 0) and interpret these numbers as slopes for the equation f(x, y) = 4 - x² - 4y². fx(1, 0) = __ and fy(1, 0) = __.

Answer 1

The slope fx(1,0) of the function f(x,y) = 4 - x² - 4y² at the point (1,0) is -2, and the slope fy(1,0) is 0.

Step-by-step explanation:

To find fx(1,0) and fy(1,0) for the equation f(x,y) = 4 - x² - 4y², we need to take partial derivatives with respect to x and y.

Taking the partial derivative with respect to x, fx, means treating y as a constant and differentiating only with respect to x. Therefore, fx = -2x.

Taking the partial derivative with respect to y, fy, means treating x as a constant and differentiating only with respect to y. Therefore, fy = -8y.

So, fx(1,0) = -2(1) = -2, and fy(1,0) = -8(0) = 0.