00:01
Hello students, here it is given a cost function where the cost function is c of x equal to 0 .01 x cube plus 0 .2 x square plus 60 x plus 130 and it is given that x is 0 less than or equal to x less than 1500 and a equal to 500.
00:35
Here first we have to find the average cost and marginal cost.
00:52
We know that average cost is it is average cost which is denoted by c bar which is equal to c of x by x.
01:05
Here we can write it as 0 .01 x cube plus 0 .2 x square plus 60 x plus 130 by x.
01:23
By solving this we will get the average cost which is c bar equal to 0 .01 x square plus 0 .2 x plus 60 plus 130 by x.
01:47
Next we have to find the marginal cost that is marginal cost equal to here the marginal cost is c dash of x which is equal to d c of x by d x that is we have to differentiate c of x that is by differentiating d by d x of the cost function is 0 .01 x cube plus 0 .2 x square plus 60 x plus 130 by differentiating this we will get 0 .03 x square plus 0 .4 x plus 60.
02:44
Hence we can say that the marginal cost is which is c dash of x is 0 .03 x square plus 0 .4 x plus 60.
03:02
Next we have to find the average and marginal cost at x at a equal to 500 that is we have to substitute x equal to 500 in average cost and marginal cost that is x equal to 500 the average cost will be 0 .01 into 500 plus 0 .2 into 500 plus 60 plus 130 by 500.
03:46
By solving this we will get the average cost which is 165 .26...