Question

The curve y = x^1/5 has at (0, 0):
1. A vertical tangent (parallel to the y-axis).
2. A horizontal tangent (parallel to the x-axis).
3. An oblique tangent.
4. No tangent.

Answer 1

Correct Answer - Option 2 : A horizontal tangent (parallel to the x-axis).

Concept:

The slope of the tangent to the curve y = f(x) at a point (a, b) is given by m = \(\rm \left(\frac{dy}{dx}\right)_{(a,b)}\).

 

Calculation:

The given equation of the curve is y = x1/5.

The slope of the tangent at (0, 0) will be given by:

m = \(\rm \left(\frac{dy}{dx}\right)_{(0,0)}=\left(\frac{1}{5}x^{-\frac45}\right)_{(0,0)}\) = 0.

Since the slope of the tangent is 0, it is horizontal (parallel to the x-axis).