Suppose that c (x )equals 7 x cubed minus 70 x squared plus 13 comma 000 x is the cost of manufacturing x items. Find a production level that will minimize the average cost of making x items.

A production level that will minimize the average cost of making x items is x=5.

Step-by-step explanation:

Given that

is the cost of manufacturing x items

To find a production level that will minimize the average cost of making x items:

The average cost per item is

Now  we get

f(x) is continuously differentiable for all x

Here x≥0 since it represents the number of items.,

Put x=0 in

For x=0 the average cost becomes 13000

∴ f(0)=13000To find Local extrema :

Differentiating f(x) with respect to x

∴  x=5 gives the minimum average cost .At x=5 the average cost is

∴ f(5)=12825 which is smaller than for x=0 is 13000∴ f(x) is decreasing between 0 and 5 and it is increasing after 5.