Question

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

• A. –3
• B. –2
• C. –1
• D. 0

Answer 1

Answer: (A)

–3

Answer 2

Equation of tangent at (1, 1) is

y – 1 = (2 + b) (x – 1) for first quadrant b < 0 \ Area = 2 $\frac { 1 } { 2 } \times \frac { b + 1 } { b + 2 }$× (–1 – b) = 2 Ž (b + 1)² + 4b + 8 = 0 Ž b² + 6b + 9 = 0

Ž (b + 3)² = 0 \ b = – 3.