Question

If P(x₁, y₁), Q(x₂, y₂) be any two points on the curve y = 3x – 2 – x² for 1 < x < 2, then the minimum value of

3x₁+3x₂ –$x_{1}^{2}$ – $x_{2}^{2}$ is-

• A. 9
• B. 4
• C. 2
• D. 9/2

Answer 1

Answer: (D)

9/2

Answer 2

$\frac{y_{1} + y_{2}}{2}$£ max (y)

y₁ + y₂ £ 2$\left( \frac{9}{2} - 2 - \frac{9}{4} \right)$

3x₁ + 3x₂ – $x - y + 2 = 0$ – $x = y - 2$ £ 9/2