Question

The cost C (in dollars) of manufacturing x number of high-quality computer laser printers is C=15x^(4/3)+54x^(2/3)+600000. Currently the level of production is 1728 printers and that level is increasing at the rate of 350 printers each month. Find the rate at which the cost is increasing each month.

Answer 1

you need to differentiate the equation for Cost

Answer 2

so you will end up with something like:\[C=f(x)\implies\frac{dC}{dx}=f'(x)\]this can be rearranged to get:\[dC=f'(x)\cdot dx\]

Answer 3

you can then use this to get the rate at which cost is increasing \(dC\)

Answer 4

A solution is attached.