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The least positive integral value of 'k'...

The least positive integral value of `'k'` for which there exists at least one line that the tangent to the graph of the curve `y=x^(3)-kx` at one point and normal to the graph at another point is

A

`2`

B

`4`

C

`3`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
A
Tangent at `(t,t^(3)-kt)` is `y=(3t^(2)-k)x-2t^(3)`
This line cuts the curve again at `x=-2t` where slope of tangent is `12t^(2)-k`
`implies(12t^(2)-k)(3t^(2)-k)=-1`
for positive root `Dge0implies9(3k-4)(3k+4)ge0`
`kepsilon(4/2,oo)implies` Ans `2`
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