Sum

Price P for demand D is given as P = 183 +120D - 3D^{2} Find D for which the price is increasing

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#### Solution

Price function P is given by

`"P" = 183 + 120"D" - 3"D"^2`

Differentiating w.r.t. D

`"dP"/"dD"=120-6D`

If price is increasing then we have `"dP"/"dD">0`

∴ 120 - 6D > 0

∴ 6D < 120

∴ D < 20

∴ The price is increasing for D < 20.

Concept: Increasing and Decreasing Functions

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