The revenue R for a company selling x units is $R = 900 x - 0.3 x ^ { 2 }$ . Use differentials to approximate the change in revenue if sales increase from $x = 1000$ to $x = 1100$ units.
A)24,000 dollars
B)30,000 dollars
C)25,000 dollars
D)29,000 dollars
E)40,000 dollars

Question

Quizplus · Accepted Answer

To approximate the change in revenue, $\Delta R$, as sales increase from $x = 1000$ to $x = 1100$, we use the differential of the revenue function, $dR$. First, find the derivative of $R$ with respect to $x$, $R' = 900 - 0.6x$. At $x = 1000$, $R' = 900 - 0.6(1000) = 900 - 600 = 300$. The change in $x$, $\Delta x$, is $1100 - 1000 = 100$. Thus, $dR = R' \Delta x = 300(100) = 30,000$ dollars.

The Revenue R for a Company Selling X Units Is R=900x−0.3x2R = 900 x - 0.3 x ^ { 2 }R=900x−0.3x2

The Revenue R for a Company Selling X Units Is $R = 900 x - 0.3 x ^ { 2 }$