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Question
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
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Solution
The given function is p = `183 + 120 D – 3D^2`
∴ `(dp)/(dD)=120-6D`
Now `(dp)/(dD)`=`0⇒120-6D=0⇒D=20`
For increasing the price
`(dp)/(dD)>0`
`120-6D>0`
`-6D>-120`
`D<120/6`
`D<20`
Demand and price cannot be negative
∴ Price is increasing in the internal (0, 20).
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