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# Instantaneous Rate of Change of Demand with Respect to Price

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Suppose that the demand for a product depends on the price (p) according to:

D(P) = 40,000/p^3 - 1/4, p>0

where p is in dollars. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when p = 50.

Please provide a step by step help.

https://brainmass.com/math/calculus-and-analysis/instantaneous-rate-change-demand-respect-price-333825

## SOLUTION This solution is FREE courtesy of BrainMass!

As the demand for a product depends on the price (p) according to:

D(P) = 40,000/p^3 - 1/4, p>0

so,

D'(p)=-120,000/p^4

Thus, the instantaneous rate of change of demand with respect to price when p = 50 is

D'(50)=-120,000/50^4
=-0.0192

That means when the price p increases by 1 dollar, then the demand will decrease by 0.0192 units.

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