Question

Assume that the profit generated by a product is given by where x is the number of units sold. If the profit keeps changing at a rate of per month, then how fast are the sales changing when the number of units sold is 1100? (Round your answer to the nearest dollar per month.) $30/month $132,665/month $16,583/month $33,166/month

Answer 1

Answer:

P'(1100)=0.06

(see explanation below)

Step-by-step explanation:

The answer is incomplete. The profit function is missing, but another function will be used as an example (the answer will not match with the options).

The profit generated by a product is given by $P=4\sqrt{x}$.

The changing rate of sales can be mathematically expressed as the derivative of the profit function.

Then, we have to calculate the derivative in function of x:

$\dfrac{dP}{dx}=\dfrac{d[4x^{0.5}]}{dx}=4(0.5)x^{0.5-1}=2x^{-0.5}=\dfrac{2}{\sqrt{x}}$

We now have to evaluate this function for x=1100 to know the rate of change of the sales at this vlaue of x.

$P'(1100)=\frac{2}{\sqrt{1100} } =\frac{2}{33.16} =0.06$