Practicing Success
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 |
-1 3 -3 1 |
-3 |
$f(x)=x^2+b x-b \Rightarrow f'(x)=2 +b $ ∴ $f'(1)=2+b$ ∴ Equation of tangent at (1, 1) is y – 1 = (2 + b) (x – 1) ⇒ (b + 2) x – y – (b + 1) = 0 ∴ Length of x-intercept = $\frac{b+1}{b+2}$ Length of y-intercept = – (b + 1) ∴ Area of triangle = $-\frac{1}{2} \frac{b+1}{b+2}$ (b + 1) = 2 (given) ⇒ b2 + 6b + 9 = 0 ⇒ b = -3 Hence (3) is the correct answer. |