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प्रश्न
The curve y = `x^(1/5)` has at (0, 0) ______.
विकल्प
A vertical tangent (parallel to y-axis)
A horizontal tangent (parallel to x-axis)
An oblique tangent
No tangent
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उत्तर
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.
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