   # Find the area of the largest rectangle that will fit inside the region bounded by y = - x^2 +1 and y = x^2 ?

+1 vote
104 views

Find the area of the largest rectangle that will fit inside the region bounded by y = - x^2 +1 and y = x^2 ?  posted Aug 25, 2018
Share this puzzle

## 1 Answer

0 votes

If A is the area of the required rectangle between the 2 parabola, then
A/2 = (-x^2 + 1 - x^2)×x
A/2 = -2x^3 + x ---- 1
Now differentiating wrt x and equating it to 0
-6x^2 + 1 = 0
x = +/-(1/(6^0.5)) --- 2
Sub 2 in 1
A/2 = 2/(3×(6^0 5))
A = 4/(3×(6^0.5)) is the max area possible for a rectangle between the 2 parabolas with dimensions (2/6^0.5) & (2/3). answer Sep 25, 2018

Similar Puzzles
0 votes

A helicopter is flying along the curve given by y = x^2 + 7. A soldier placed at (3,7) wants to shoot down the helicopter. He would find it feasible to do so when It is closest to him. Find this closest distance at which he can shoot the helicopter.

+2 votes
1. What would be the coordinate of point P which divides the line joining A(-4,1) and B (17,10) in the ratio 1:2?
2. What would be the length of OP where O is the origin (0,0)?
3. In what ratio y axis divides the line segment AB?