The curve passes through the point

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

The curve

x^{2}y + y^{3} = 6

passes through the point

(1,\sqrt{2})

. Determine whether the tangent line to the curve at this point is horizontal, vertical, or neither. State the value of

\dfrac{dy}{dx}

used to reach your conclusion.