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 1900

Answer 1

21794.495 units/month

Explanation:

Some data are missing which i can assume as per requirement of the Question.

Let us consider that profit generated by a product is given by

p(x) =4√x

Also, consider that the profit keeps changing at a rate of $1000 per month.

Now, Using the chain rule we can write

dp/dx=(dp/dt)÷(dx/dt).

So, we can calculate

dp/dx=2x^(-1/2)=2/√x.

As per question we have to find out dx/dt

Since, dx/dt= (dp/dt)/(dp/dx),

so plugging x=1900 we get 1000√1900/2=21794.495 units/month increase in sales.