Answer 1

Revenue = Price × Demand

∴ R = p × x

∴ R = (10800 - 4x²)x

∴ R = 10800 - 4x³

∴ `"dR"/"dx" = 10800 - 12"x"^2 = 12(900 - "x"^2)`

Since revenue R is an increasing function,

`"dR"/"dx" > 0`

∴ 12(900 - x²) > 0

∴ 900 - x² > 0

∴ 900 > x² 

∴ x² < 900

∴ - 30 < x < 30

∴ x > - 30 and x < 30

But x > - 30 is not possible     ....[∵ x > 0]

∴ x < 30

∴ The revenue R is increasing for x < 30.