Question

The number of vertical tangents to the graph of y^2=x-x^3 is? Please guide me through.

Answer 1

The number of vertical tangent to
\(\large\color{#000000 }{ \displaystyle y^2=x-x^3 }\)

will be the same as the number of vertical tangents to
\(\large\color{#000000 }{ \displaystyle y=\sqrt{x-x^3} }\)

Differentiate the function, and the points where
the derivative is undefined are going to be vertical
tangents.

Answer 2

find the derivative, and set the denominator of the derivative =0.