Let C(x) be the cost of producing cars in a factory
Find the formula A(x), the average price of producing a car in the factory when x cars are being produced
Let C(1)=100$
C(2)=200$
C(3)=300$...
To find the average all we need to do is add 2 prices then divide by 2
so 100$+200$=300$
300$/2=150$
The average price is 150$ for one car
So A(1)=150$
for A(2)=200$+300$=500$/2=250$
Hence the ratio of change is 100$
Now to write A(x) in terms of x
A(x)=((C(x)+C(x+1)/2
To test the function we use C(1) and C(2)
A(1)=((C(1)+C(2))/2 (100+200)/2=150
So it works!
Now to derive We know A(x)=((C(x)+C(x+1))/2
So we derive that, after deriving that and simplify we Get \(d/dx(1/2 (C(x)+C(x+1))) = 1/2 (C'(x)+C'(x+1)) \)
Now deriving C(x) we get \(C'(x)\) Sorry if i got some of the derivatives wrong
