A company's revenue from selling x units of an item is given as R=1000x−2x2. If sales are increasing at the rate of 20 units per day, how rapidly is revenue increasing (in dollars per day) when 210 units have been sold?
R=1000x−2x^2
dR/dt = 1000 dx/dt - 4x dx/dt
but dx/dt = 20 units/day
so when x = 210 units
dR/dt = 1000(20) - 4(210)(20) = 3200 dollars/day