Question

Suppose that g(x, y) = x^2+ y^2−1 and f (x, y) = y −ax for some

number a, and that you wish to find the point on the circle with
equation g(x, y) = 0 at which f (x, y) is largest. Explain briefly

Answer 1

The point on the circle where f(x, y) is largest is (0, 1).

Step-by-step explanation:

To find the point on the circle where f(x, y) is largest, we need to find the maximum value of f(x, y). Since f(x, y) = y - ax, the maximum value occurs when y is at its maximum and ax is at its minimum. The equation g(x, y) = x^2 + y^2 - 1 represents a circle, so the point on the circle where f(x, y) is largest will be the point where ax is minimized. The minimum value of ax occurs at the center of the circle, which is (0, 0). Therefore, the point (0, 1) on the circle g(x, y) = 0 is where f(x, y) is largest.