Assertion (A) : The tangent to the curve `y=x^(3)-x^(2)-x+2` at (1,1) is parallel to the x - axis ltrbgt Reason (R ): The slope of the tangent to the cuve at (1,1) is zero

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is the correct expantation of A
C. A is true but R is false
D. A is false but R is true

Answer

A

Explanation

Given equation of the curve is y `=x^(3)-x^(2)-x+2`
`(dy)/(dx)=3x^(2)-2x-1` ltbr?gt `rarr ((dy)/(dx))_(1,1)=3-2-1=0`
`since ,(dy)/(dx) at (1,1) is 0`
`therefore` slope of the tangent =0
Hence The equation of tangent at (1,1) is
`y-1 =0(x-1) rarr y=1`
ie parallel to x axis
Both A and R true and R is the correct expalnation of A