The triangle formed by the tangent to the curve `f(x)=x^2+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`

Options

A. `-1`
B. `-(5)/(2)`
C. `-3`
D. 1

Answer

C

Explanation

Since, tangent at (1,1) to the parabola forms a triangle with axis, which lie in the first quadrant, vertex lies to the ringt of x=1.
`therefore-(b)/(2)gt1impliesblt-2`

Equation of tangent at (1,1) is
`y-1=(b+2)(x-1)`
`therefore`x-intercept`=((b+1))/(b+2)`
y-intercept=-(b+1)
`therefore` Area of `Delta=-((b+1)^(2))/(2(b+2))=2`
`impliesb^(2)+6b+9=0`
`impliesb=-3`.