Question

The triangle formed by the tangent to the curve \( y = x^2 + x + 1 \) at the point \( (1, 3) \) 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. 6
• D. None of these

Hint:

To find the equation of the tangent line, use the point of tangency and the derivative at that point.

Answer 1

The Correct Option is C

The equation of the tangent to the curve is given by the derivative at the point of tangency. The area of the triangle formed by the tangent line and the coordinate axes can be calculated, and the value of \( b \) is found to be 6.