Sum

The price P for demand D is given as P = 183 + 120 D – 3D^{2}.

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).

Concept: Increasing and Decreasing Functions

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