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

JEE MATHEMATICS MCQ: TANGENTS & NORMALS

1 Easy

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Analyzing +4 | -1

The curve

y=x^{\frac{1}{5}}

(0,0)

has

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Correct option: B

a horizontal tangent (parallel to

x

aria)

Option A (a vertical tangent (parallel to y-axis)) is correct because the derivative approaches infinity at (0,0), indicating a vertical tangent.

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a

y=x^3-a x

x^2 y=1-y

x y=1-y

C

y^3-3 x y+2=0

H

\mathrm{C}

x

V

C

y

y-e^{x y}+x=0

y = f\left( x \right)

x

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z