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Find the point on the curve y=x^3-11 x+5...

Find the point on the curve `y=x^3-11 x+5` at which the tangent is `y" "=" "x" "" "11` .

A

`(2,19)`

B

`(1,-5)`

C

`(-4,-15)`

D

`(2,-9)`

Text Solution

Verified by Experts

The correct Answer is:
D
Let point on `y=x^(3)-11x+5` is `(alpha,beta)`
`:.beta=alpha^(3)-11alpha+5`
Now `(dy)/(dx)=3x^(2)=11:.m=3alpha^(2)-11`
`:.3a^(2)-11=1impliesalpha^(2)=4impliesalpha=+-2`
`:.` points on curve are `(-2,19)` and `(2,-9)`
but `(-2,19)` does not lie on `y=x-11`
`:.(2,-9)` is required point
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