Question:

Let S be the set of all values of x for which the tangent to the curve y=f(x)=x³-x²-2x at (x, y) is parallel to the line segment joining the points (1, f(1)) and (-1, f(-1)), then S is equal to?

-1;3,1

-1;3,-1;

13,-1;

13,1

Correct option is C. -1;3,1
f(1)=1-1-2=-2
f(-1)=-1-1+2=0
m=f(1)-f(-1)/1+1=-2-0/2=-1
dy/dx=3x²-2x-2
3x²-2x-2=-1
3x²-2x-1=0
(x-1)(3x+1)=0
x=1,-1/3.