The points on the curve `y=x^(3)-x^(2)-x+3`, where the tangents are parallel to the X-axis, are `(+1/3,(-88)/27)` and (1,2)

Answer

B

Explanation

Given `y=x^(3)-x^(2)-x+3`…………….i
`implies(dy)/(dx)=3x^(2)-2x-1`
`implies(dy)/(dx)=3x^(2)-2x-1`
Tangent is parallel to the X-axis.
`:.(dy)/(dx)=0`
`implies3x^(2)-2x-1=0impliesx=-1/3` or 1
For `x=-1/3`
`y=(-1/3)^(3)-(-1/3)^(2)-(-1/3)+3=86/27`
for `x=1, y=1^(3)-1^(2)-1+3=2`
Hence the required points are `(-1/3, 86/27)` and (1,2)