00:01
Okay, so to find the rate of change of the total cost c, which we denote dc dt with respect to time, we will need to use related rates calculus.
00:12
Now, given the relationship between c and q, cq plus 2q squared equals 7642.
00:21
2, and knowing that q is in hundreds of units, so we have that q is equal to 15 when 1500 units are being produced.
00:38
So we are given that dq dt is equal to 0 .77.
00:45
Now this is because q is in hundreds of units, and 77 units per week corresponds to 0 .77 hundreds units per week.
00:54
Now, we need to differentiate both sides of the equation here with respect to time to find the value dc dt.
01:06
So, we have a d dt c cube plus 2 cube squared equals d dt 7640.
01:19
Zero, we know that the right -hand side is equal to zero, and the left -hand side is equal to 3c squared times dc, dt, plus 4q times dq, dt, which is equal to zero...