If y=√[3]6 x y2-11 x2 y+6 x3, then possible value(s) of (d y/d x) at x=2 is(are)

Question

If y=√[3]6 x y2-11 x2 y+6 x3, then possible value(s) of (d y/d x) at x=2 is(are) (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

y=√[3]6 x y2-11 x2 y+6 x3 y3=6 x y2-11 x2 y+6 x3 y3-6 x y2+11 x2 y-6 x3=0 ⇒(y-x)(y-2 x)(y-3 x)=0 ⇒ y=x, y=2 x, y=3 x ∴ (d y/d x)=1,2,3

Q. If $y = 3 6 x y^{2} - 11 x^{2} y + 6 x^{3}$ , then possible value(s) of $\frac{d y}{d x}$ at $x = 2$ is(are)