Answer:
dx/dt = 12 (in thousands of units /week)
Step-by-step explanation:
We have from problem statement that:
8*p³ + x² = 104 (1)
Where p is price in $, and "x" is the weekly sales in thousands of units
All variables x and p change in relation to time then
Differentiating on both sides of the equation, we get:
24*p²*dp/dt + 2*x*dx/dt = 0 (1)
We need to find dx/dt and we know
p = 20
x = 200
And price is falling at the rate of 0,5 $/week
Then plugging these values in equation (1)
24*p²*dp/dt = - 2*x*dx/dt
24*(20)²(-0,5) = -400*dx/dt
-4800 = -400*dx/dt
dx/dt = 4800/400
dx/dt = 12 (in thousands of units /week)
