Question

The curve $$ y=x^{\frac{1}{5}} $$ has at $$ (0,0) $$

Answer 1

Correct option is A. a vertical tangent (parallel to y-axis)

We have, $$ y=x^{1/5} $$

$$ \Rightarrow \dfrac{dy}{dx}=\dfrac{1}{5}x^{\tfrac{1}{5}-1}=\frac{1}{5}x^{-4/5} $$

$$ \therefore \left( \dfrac { dy }{ dx } \right) _{ (0,0) }= \tfrac{1}{5} \times (0)^{-4/5}= \infty $$

So, the curve $$ y=x^{1/5} $$ has vertical tangent at $$ (0,0) $$, which is parallel to y-axis.