The curve y `= x^((1)/(5))` has at (0,0)

Options

A. a vertical tangent (parallel to Y-axis)
B. a horizontal tangent (parallel to X-axis)
C. an oblique tangent
D. no tangent

Answer

A

Explanation

We have, `y=x^(1//5)`
`rArr (dy)/(dx)=1/5x^(1/5-1)=1/5x^(-4/5)`
`therefore (dy)/(dx)_(0,0)=1/5 xx (0)^(-4/5) = infty`
So, the curve `y=x^(1//5)` has a vertical tangent at (0,0), which is parallel to Y-axis.