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Question: If P (x<sub>1</sub>, y<sub>1</sub>), Q (x<sub>2,</sub> y<sub>2</sub>) be any two points on the curve...

If P (x1, y1), Q (x2, y2) be any two points on the curve

y = 3x – 2 – x2 for 1 < x < 2, then maximum value of

3x1 + 3x2 – x12 – x22 is-

A

9

B

4

C

2

D

92\frac{9}{2}

Answer

92\frac{9}{2}

Explanation

Solution

y1+y22≤\frac{y_{1} + y_{2}}{2} \leq max. (y)

y1 + y2 £ 2 (92−2−94)\left( \frac{9}{2} - 2 - \frac{9}{4} \right)

3x1 + 3x2 – x12 – x22 £ 92\frac{9}{2}