for the curve C x^{3} + xy + 2y^{3} =k , the y co-ordinates of the tangent parallel to the y axis is given by
216y^{6 }+4y^{3} +k = 0
Show that k<= 1/54
For the other question, differentiate both sides of the original equation:
If the line is a tangent at the point (x,y), it means that x = -6 and dy/dx is undefined, i.e. the denominator of dy/dx is zero. This occurs only when . So try substituting (1,6) and (-1,6) into your original equation and find k.