Question

The demand function of a commodity is given as P = 20 + D − D². Find the rate at which price is changing when demand is 3.

Answer 1

Given, P = 20 + D – D²

Rate of change of price = ${\displaystyle \frac{\text{dP}}{\text{dD}}}$

= ${\displaystyle \frac{\text{d}}{\text{dD}}(20+\text{D}-{\text{D}}^2)}$

= 0 + 1 – 2D
= 1 – 2D
Rate of change of price at D = 3 is

${\displaystyle {\left(\frac{\text{dP}}{\text{dD}}\right)}_{\text{D}=3}}$

= 1 – 2(3)
= – 5
∴ Price is changing at a rate of – 5 when demand is 3.