The revenue R for a company selling x units is R = 700x − 0.1x^2.?
(a) Use differentials to approximate the change in revenue as the sales increase from 3000 units to 3100 units.
dR = $
(b) Compare this with the actual change in revenue.
ΔR = $
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(a)
R = 700x - 0.1x^2
R' = 700 - 0.2x
dR = R'dx
= (700 - 0.2x)dx
dx = 3100 - 3000 = 100
dR = (700 - 0.2*3000)*100
= 10000
(b)
∆R = [700(3100) - 0.1(3100)^2] - [700( 3000) - 0.1(3000)^2]
= 1209000 - 1200000
= 9000