The triangle formed by the tangent to the curve f(x) = x² + bx - b at the point (1,1) and the coordinate axes, lies in the first quadrant. If its area is 2, then the value of b is

a) -1 b) 3 c) -3 d) 1

Hi Raghu,

Eqn of tangent at (1,1) is

(y-1) = (b+2)(x-1)

Points where it will intersect the co-ord axis is: (0,-b-1) and ([b+1]/[b+2],0) ------- {obtained by putting x=0 and y=0 in the tangent equation}

So 1/2*|-b-1|*|(b+1)/(b+2)| = 2 or (b+1)²/|b+2| = 4.

Clearly b=-3.

Option (C).

Regards,

Ashwin (IIT Madras).

Approved