Question

The triangle formed by the tangent to the curve $f\left(x\right)=x^2+bx-b$ at the point (1, 1) and the co-ordinate 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

Answer 1

The correct option is C -3

$\frac{dy}{dx}=2x+b=x+bat(1,1)$
Equation of tangent is $y-1=(2+b)(x-1)$ is intercepts A and B on the axis are obtained by putting y = 0 and then x = 0
$\therefore A\frac{b+1}{b+2},B=-(b+1)\Delta =\frac{1}{2}AB=2\therefore AB=4\Rightarrow -(b+1)(b+1)=4(b+2)\therefore b=-3$