Final answer:
To find the equation of the level curve of the function f(x, y) = x²y that passes through the point (1, -2), substitute the given point into the equation and solve for the unknown constant.
Step-by-step explanation:
To find the equation of the level curve of the function f(x, y) = x²y that passes through the point (1, -2), we need to substitute the given point into the equation and solve for the unknown constant. Let's do that:
Substituting (1, -2) into the equation, we have -2 = 1² * (-2). Simplifying this, we get -2 = -2.
Since the left side of the equation is equal to the right side, we have found the equation of the level curve passing through the given point: -2 = -2.