The curve defined by passes through the origin

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

Problem

The curve defined by

y^{2}=x^{3}-x

passes through the origin. Determine whether the tangent line to the curve at

(0,0)

is vertical by evaluating

\dfrac{dy}{dx}

at that point. State your conclusion and justify it numerically.