Question

the gradient of the curve y-xy+2px+3qy=0 at the point (3,2) is -2/3 the value of p & q are??

Answer 1

Question #16187

The gradient of a function $f(x, y) = y - xy + 2px + 3qy$ is $\nabla = (-y + 2p; 1 - x + 3q)$ . Given, that it is equal to $(-2; 3)$ at point $x = 3, y = 2$ , obtain $-2 + 2p = -2; 3q - 2 = 3$ , which gives $p = 0, q = \frac{5}{3}$ .