Question

The cost
C
(in dollars) of manufacturing
x
number of high-quality computer laser printers is
C
(
x
)
=
12
x
4
/
3
+
9
x
2
/
3
+
500
,
000

Currently, the level of production is
1
,
728
printers and that level is increasing at the rate of
300
printers per month. Find the rate at which the cost is increasing each month.

The cost is increasing at about
$
per month.

Answer 1

\(\color{yellow}{C(x)}= \color{lime}{\dfrac{12x^4}{3}} + \color{cyan}{\dfrac{9x^2}{3}} + \color{violet}{500,000}\)

So to find how much it will cost per month,
x is going to be 300 so,

\(\color{yellow}{C(x)}= \color{lime}{\dfrac{12(500)^4}{3}} + \color{cyan}{\dfrac{9(500)^2}{3}} + \color{violet}{500,000}\)

Answer 2

unless i read this wrong and it's

\(\color{yellow}{C(x)}= \color{lime}{\dfrac{12\times4}{3}} + \color{cyan}{\dfrac{9\times2}{3}} + \color{violet}{500,000}\)

but that doesn't give you an \(x\) variable to change.