Find the point c in the curve f(x) = x^3 + x^2 + x + 1 in the interval [0, 1] where slope of a tangent to a curve is equals to the slope of a line joining (0,1) (2 marks)
- A. 0.64
- B. 0.54
- C. 0.44
- D. 0.34
Answer: B. 0.54
Explanation: By Lagrange's Mean Value Theorem, f'(c) = [f(3) - f(0)] / 3. Solving 3c² + 2c + 1 = 2.92 yields c ≈ 0.54 in (0, 1).