00:02
In this question, we are asked to find the cost function and we are given the marginal cost as 10 plus x plus 1 over x squared.
00:21
And we are given the total cost to produce 100 boxes that is c of 100 is equals to $90 ,000.
00:31
So we are asked to find the cost function c of x.
00:37
So we are given the marginal cost which is nothing but c dash of x is equals to 10 plus x plus 1 over x squared.
00:49
So we are asked to find c of x.
00:54
So we have to apply integration.
00:56
So integration of c dash of x is equals to integral of 10 plus x plus 1 over x squared dx.
01:05
So we'll be getting 10x plus x squared over 2 plus for integration of 1 over x squared.
01:18
Let's write it as x negative of 2 dx which is going to be x to the power of negative 2 plus 1 over negative 2 plus 1 which is going to be x to the power of negative 1 over negative 1.
01:33
So this is actually x to the power of negative 1 over negative 1 plus c.
01:41
So i'm going to write this as c of x is equals to 10x plus x squared over 2.
01:49
This can be written as negative of 1 over x plus c.
01:54
So we are already given that c of 100 is equals to $90 ,000.
01:59
So let's write this...