Find points at which the tangent to the curve `y=x^(3)-3x^(2)-9x+7` is parallel to the x-axis

Options

A. `(3, -20)` and `(-1, 12)`
B. `(3, 20)` and `(1, 12)`
C. `(3, -10)` and `(1, 12)`
D. None of these

Answer

A

Explanation

Slope `(dy)/(dx)=3 x^(2)-6x-9`
it tangent is parallel to the x-axis then `(dy)/(dx)=0`
`rArr 3x^(2)-6x-9=0 " " rArr x^(2)-2x-=0`
`rArr x^(2)-3x+ +x-3=0 " " rArr (x-3)(x+1)=0`
`rArr x=3` or `x=-1 " " rArr y=-20` or `y=12`