Question

The curve y = x^1/5 has at (0, 0)

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

B. a horizontal tangent (parallel to x-axis)

C. an oblique tangent

D. no tangent

Answer 1

Given y = x^1/5

Differentiating both sides with respect to x, we get

Now at (0,0), the above equation becomes

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

Hence the correct option is option A.