00:01
Hello, i have a question.
00:02
This is that an open box is to be made out of a 6 inch by 20 inch piece of cardboard.
00:11
Okay, like this.
00:15
If this is 20 inch and this is 6 inch, so an open box will be made and the 4 squares are being cut from the 4 corners.
00:32
Therefore, if we have sides of a square jacks, 4 equal square.
00:38
Has to be cut this is x this is x so now the remaining width will be 6 minus 2x inches remaining length will be 20 minus 2x inches and height will be this x so i have to find uh largest volume so volume will be length 20 minus 2x into width 6 minus 2x into height so let us write it as 20 minus 2x into 6x minus 2x squared i have to maximize or minimize this so for that i have to first find the critical point and for the critical point dv by dx should be equal to 0 let us keep this up i am using the product rule of differentiation 6 minus 4x plus differentiating first term 0 minus 2 into 6x minus 2 square should be equal to 0.
02:00
Okay, so if you take 2 common from here, 2 common from here, 2 common from here, 2 common from here, or dividing both sides by 4, i will be getting 10 minus x into 3 minus 2x minus 2x minus 3 minus 3x or 3x.
02:23
Minus x squared that should be equal to 0 now this is if we take product 30 minus 3x minus 20x plus 2x square minus 3x plus x squared should be equal to 0 so 2x squared plus x squared plus x squared 3x squared and minus 26 x plus 30 should be equal to 0 i'll be using the formula of quadratic equation minus b plus minus b squared minus 4a and c k divide by 2a 2 2 into 3 so 26 plus minus i will be using the calculator to calculate that which is 26 squared k 26 square minus 360 the root which is 17 .776 divided by 6.
04:06
If you take positive sign it will become plus 26 divide by 6 which is 7 .29 7 .29 and if you take a positive sign it will become plus 26 divide by 6 which is 7 .29 7 .29 and if you take a negative sign okay, it would become 26 minus 17 .776 divided by 6 .370...