0:00
Hi.
00:01
Now given p of x is equal to minus 4 .25 x squared plus 3 ,200 x minus 6 ,500 where px is the profit function when x units are sold.
00:21
Now we have to find profit when x is equal to 70.
00:26
So now putting this here, x is equal to 70, we get minus 1 .5 .000.
00:30
4 .25 into 70 square plus 3 ,200 into 70 minus 6 ,500.
00:39
So this value comes out to be equal to 196 -67.
00:46
Now next, we have to find average profit per unit when x is equal to 70.
00:52
So average profit is equal to now from 0 to 70 p of x this is 70 p of x d x so this is equal to 0 to 70 minus 4 .25 x square plus 30 to 100 x minus 6500 d x so now on integrating this comes out to be equal to minus 4 .25 x cube by 3 plus 3200 into x square by 2 minus 6 ,500 x ranging from 0 to 70.
01:40
Now on putting the limits this comes out to be equal to 6899083 .3 .3.
01:49
3, 4.
01:51
Now we have to find the rate at which profit is changing when x is equal to 70...