Question

The slope of the tangent to the curve y^3x + y^2x^2 = 6 at (2,1)

Answer 1

Y^3x + y^2x^2 = 6 

Using implicit differentiation 

3 y^2.y'.x+y^3+2 y.y'.x^2+2 y^2.x=0
 
y'(3 y^2.x+2 y. x^2) = -y^3-2 y^2.x 

y' = -[y^2(y+2 x)]/[x y(3 y+2 x)] 

   = -[y(y+2 x)]/[x(3 y+2 x)] 

Substituting x =2 and y = 1:
 
y' = -(1)(1+4)/[2(3+4)] 
   = -5/14 

The slope of the tangent of the curve at (2,1) will be:
 m = -5/14