Question

The maximum area of a rectangle whose two vertices lie on the x-axis and two on the curve y = 3 – |x|, – 3 ≤ x ≤ 3 is

• A. 9
• B. 9/2
• C. 3
• D. None of these

Answer 1

Answer: (B)

9/2

Answer 2

The area bounded by the lines

y = 3 -|x|, – 3 ≤ x ≤ 3 is shown in the fig.

Area A(x) = 2x .(3-x)

⇒ A′(x) = 2 (3-x) –2x

= 6 – 4x = 0 ⇒ x = 3/2

⇒ Maximum area of the rectangle occurs when x = 3/2.

Maximum area=2. $\frac { 3 } { 2 } \left( 3 - \frac { 3 } { 2 } \right) = \frac { 9 } { 2 }$ sq. units