The function gives the cost to manufacture x items. C(x) = 10,000 + 20x + 30,000 x ; x = 100 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated and h = 10 and 1. (Use smaller values of h to check your estimates.) HINT [See Example 1.] (Round your answer to two decimal places.)

Step-by-step explanation:

Average rate of change through the formula

given that,

To find the average cost per unit of manufacturing   more items, the strategy is to apply the average rate of change to the function for   and the given    present.

when,

Average cost per unit manufacturing

when

Average cost per unit manufacturing

if

Average cost per unit manufacturing

Therefore, it can be estimated that the average rate of change of the total cost to manufacture  100  items is  $ 30020 per item (interpreted units).

Key features: the functions can not be parallels, this means that their respective slopes can not be equal or multiple to the other

Step-by-step explanation:

Take for instance 2 linear functions,  and

If they intersect in some point in the space, say that is

Then (x1,y1)=(x3,y3), (x2.y2)= (x3,y3)

So, we can compare the two functions and get the following result;

It tells us that if M=m, we get an error, meaning that the functions are in fact parallels and there is no way that they meet in some point.

hope this helps!