Question

Find all points on the curve x^2y^2+xy=2 where the slope of the tangent is -1

Answer 1

slope of tangent is just the derivative dy/dx

use implicit differentiation, solve for dy/dx , set it equal to -1

Answer 2

\[\rightarrow 2x y^{2} + x^{2} (2y) \frac{dy}{dx} + y + x \frac{dy}{dx} = 0\]

Answer 3

\[\frac{dy}{dx} = \frac{-(2xy^{2}+y)}{2x^{2}y +x} = -1\]

Answer 4

from here try to find y in terms of x , sub back into original equation , solve for x