The abscissa of the points, where the tangent to curve `y=x^(3)-3x^(2)-9x+5` is parallel to X-axis are

Options

A. x=0 and 0
B. x=1 and -1
C. x=1 and -3
D. x=-1 and 3

Answer

D

Explanation

Given `y=x^(2)-3x^(2)-9x+5`
`rArr (dy)/(dx)=3x^(2)-6x-9`
We know that, this equation gives the slop of the tangent to the curve. The tangent is parallel to x-axis.
`:. (dy)/(dx)=0`
` rArr 3x^(2)-6x-9=0`
`rArr x=-1,3`