Question

Assume that the profit generated by a product is given by P(x) = 3 x, where x is the number of units sold. If the profit keeps changing at a rate of $1000 per month, then how fast are the sales changing when the number of units sold is 600? (Round your answer to the nearest dollar per month.)

Answer 1

Answer:

D(x) / dt   ≈ - 10⁻⁷

Step-by-step explanation: Incomplete Question from google I found that the expression  P(x)  = 3 x is incorrect. The expression should be 3/√x

We assume :

P(x)  =  3 / √x         (1)

We know that  DP(x)/dt   =  1000 $/month

and

Differentiating on both sides of the equation (1)

DP(x)/dt  =  3 *  -1/2 * D(x)/dt /x√x     ⇒   DP(x)/dt  =[ -3/2x√x ] D(x)/dt

To evaluate how fast are the sales changing when the number f units (x) is  600

DP(x)/dt  =[ -3/2x√x ] D(x)/dt

1000 = [ -3/2*600*√600 ] D(x) /dt

D(x) / dt   = - 1000/1.02*10⁻⁴

D(x) / dt   ≈ - 10⁻⁷