A rectangle with its sides parallel to the X-axis and Y-axis is inscribed in the region bounded by the curves y=x^2-4 and 2y=4-x^2. The maximum…

Question

A rectangle with its sides parallel to the X-axis and Y-axis is inscribed in the region bounded by the curves y=x^2-4 and 2y=4-x^2. The maximum possible area of such a rectangle is closest to the integer.

MARKS Content Team · Accepted Answer

Correct answer: (B) 9. Equation of parabola y=x^2-4 and 2y=4-x^2 Let point B=h,(4-h^2)/2 A=-h,(4-h^2)/2 C=h_1h^2-4 D=-h,h^2-4 Area of rectangle ABCD=AB×BC=2h×(4-h^2)/2-h^2+4 ⇒A=12h-3h^3⇒dA/dh=12-9h^2 For maxima or minima dA/dh=0⇒12-9h^2=0 h=±2√3 maximum at h=2√3 ∴A=122√3-323^3=24√3-8√3 =16√3=(16√3)/3 A-(16×173)/3=9.22 A=9.22=9

A rectangle with its sides parallel to the $X$ -axis and $Y$ -axis is inscribed in the region bounded by the curves $y = x^{2} - 4$ and $2 y = 4 - x^{2} .$ The maximum possible area of such a rectangle is closest to the integer.

Solution

More Application of Derivatives Questions

A rectangle with its sides parallel to the X-axis and Y-axis is inscribed in the region bounded by the curves y=x2-4 and 2y=4-x2. The maximum possible area of such a rectangle is closest to the integer.

Solution

More Application of Derivatives Questions

A rectangle with its sides parallel to the $X$ -axis and $Y$ -axis is inscribed in the region bounded by the curves $y = x^{2} - 4$ and $2 y = 4 - x^{2} .$ The maximum possible area of such a rectangle is closest to the integer.