The points at which the tangents to the curve `y=x^(3)-12x+18` are parallel to the X-axis are

Options

A. `(2-2), (-2,-34)`
B. `(2,34),(-2,0)`
C. `(0,34),(-2,0)`
D. `(2,2),(-2,34)`

Answer

D

Explanation

The given equation of the curve is
`y=x^(3)-12x+18`
`therefore (dy)/(dx)=3x^(2)-12` [on differentiating w.r.t. x]
So, the slope of the line parallel to the X-axis .
`therefore (dy)/(dx)=0`
`rArr 3x^(2)-12=0`
`rArr x^(2)=12/3=4`
`therefore x=+-2`
For x=2, `y=2^(3)-12 xx 2+18=2`
and for `x=-2, y=(-2)^(3)-12(-2)+18=34`
So, the points are (2,2) and `(-2,34)`.