Question

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

Options

• A vertical tangent (parallel to y-axis)

• A horizontal tangent (parallel to x-axis)

• An oblique tangent

• No tangent

Answer 1

The curve y = `x^(1/5)` has at (0, 0) a vertical tangent (parallel to y-axis).

Explanation:

Equation of curve is y = `x^(1/5)`

Differentiating w.r.t. x,

We get `"dy"/"dx" = 1/5 x^((-4)/5)`

At x = 0  `"dy"/"dx" = 1/5(0)^((-4)/5)`

= `1/5 xx 1/0 = oo`

`"dy"/"dx" = oo`

∴ The tangent is parallel to y-axis.