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The Price P for Demand D is Given as P = 183 + 120 D – 3d2. Find D for Which the Price is Increasing. - Mathematics and Statistics

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Sum

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).

Concept: Increasing and Decreasing Functions
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