00:04
Given to us, rx is equal to 4x which is the total revenue in dollars.
00:09
Cx is equal to 0 .01x square wherein we add 0 .2x to which we add 20 which is the total cost in dollars.
00:17
The value of x is 25 which is number of units produced and dx by dt is equal to 9 units per day.
00:26
It is the rate at which x is changing with respect to time.
00:28
So, dr by dt is equal to 4d multiplied by 4x divided by dt.
00:40
So, we can write it as 4 multiplied by dx by dt putting x is equal to 25 and dx by dt is equal to 9.
00:52
So, dr by dt is equal to 4 multiplied by 9 we get it as 36 dollars per day.
01:06
Further, sorry, it is said to be the rate of change of total revenue is 36 dollars per day.
01:32
Then, dc by dt is evaluated as t bracket 0 .01x square wherein we add 0 .2x to which we add 20 which is then divided by dt.
01:51
Then, we can write it as 0 .02x multiplied by dx by dt to which we add 0 .2 multiplied by dx by dt.
02:08
Substitute x is equal to 25 and dx by dt is equal to 9.
02:13
So, 0 .02 multiplied by 25 to which we add 9 to which we add, sorry, which is then multiplied by 9 to which we add 0 .2 multiplied by 9...