The cost, in dollars, of producing x belts is given by C(x)...

The cost, in dollars, of producing x belts is given by C(x) = 916 + 18x - 0.077x^2. Find the rate at which average cost is changing when 324 belts have been produced. When 324 belts have been produced, the average cost is changing at dollars per belt for each additional belt. (Round to four decimal places as needed. Do not include the $ symbol in your answer.)

Transcript

00:01 Hi, here we have the following problem.

00:03 Let me zoom in a little bit.

00:05 It says the cost in dollars of producing x belts is given by this function.

00:13 I've written this function here.

00:14 This is the cost of producing x belts.

00:17 Find the rate at which average cost is changing when 320 fold belts have been produced.

00:25 So here is this what we have to do.

00:28 First, we have to find the rate at which average cost is changing when 320 fold belts have been produced.

00:29 So here is this what we have to do.

00:29 First, we have to find what is the average cost.

00:32 So average cost i'm going to write it as average cost of x by definition is the cost function divided by x where x is the quantity, the number of units produced.

00:49 So then our function is going to be the average cost function, 916 over x plus 18 minus 0 .0 .0 .0.

01:02 077 x so really what we do we take this function c of x this expression and we divide it by x we divide this term by x we get this 18 x over x we get 18 and this over x we get that okay so for the rate of we have to calculate the derivative of the average cost so if we're going to find the range to each the average cost so if we're going to find the range to each the average cost is changing, we have to calculate the derivative and here we have the derivative of the average cost is minus 916 over x square.

01:43 Don't forget that.

01:45 The derivative of 1 over x is minus 1 over x square...

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