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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.

    © BrainMass Inc. brainmass.com December 24, 2021, 9:00 pm ad1c9bdddf
    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.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 9:00 pm ad1c9bdddf>
    https://brainmass.com/math/calculus-and-analysis/instantaneous-rate-change-demand-respect-price-333825

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