okla 發問時間: 科學數學 · 1 0 年前

微積分的問題~~急 隱含微分

When the price of acertain commodity is p dollars per unit ,consumers demand x hundred units of the commodity,where 75x²+17p²=5300

how fast is the demand x chaning with respect to time when the price is 7 and is decreasing at the rate of 75 cents per month? (that is dp/dt =-0.75)

1 個解答

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  • 1 0 年前
    最佳解答

    p=7, dp/dt=-0.75

    關係 75x^2+17p^2=5300

    求 dx/dt.

    [Sol.]

    150x dx/dt + 34p dp/dt = 0

    p=7 ==> 75x^2+17(7^2)=5300 ==> x=7.7

    150(7.7) dx/dt +34(7)(-0.75)=0

    dx/dt = 34(7)(0.75)/[150(7.7)] = 0.15(百單位/月)

    需求量每月增加15單位 (或 15.4單位).

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