00:01
In this problem, we are giving that the cost function, let's write it out, c of x, is equal to 40 ,000 plus 100x, plus x to the third powered, and the revenue function, r of x, is given to equal to 5800x.
00:24
The profit function can be written as, remember that the profit function is a revenue function, minus the cost function that is r of x which is 5800 x minus the cost function so it's minus 40 ,000 minus 100 x minus x to the third powered so we can write that the profit function would equal to negative x third powered plus 5700 x minus 40 ,000 when we find the marginal profit, that is the derivative of the profit function, this would equal to negative 3x squared plus 5 ,700.
01:15
And we set this equal to 0, and then we solve for x.
01:19
So from here, we get that x is going to equal to 10 radical 19th...