I Man 發問於 科學及數學數學 · 1 十年前

# 數學題1........

1. When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x hundred units, where

3p^2-x^2=12

How fast is the quantity supplied changing with respect to time when the price is \$4 per unit and the price is increasing at the rate of 87 cents (\$0.87) per week with respect to time?

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• 1 十年前
最愛解答

1. When the price of a certain commodity is p dollars per unit, the manufacturer is willing to supply x hundred units, where

3p^2-x^2=12

How fast is the quantity supplied changing with respect to time when the price is \$4 per unit and the price is increasing at the rate of 87 cents (\$0.87) per week with respect to time?

3p^2-x^2=12

d/dt (3p^2-x^2)=0

(6p)(dp/dt)-2x(dx/dt)=0...(*)

when p=4

3(4)^2-x^2=12

x=6

ALSO dp/dt=0.87

substitute this information into (*)

(6*4)(0.87)-2(6)(dx/dt)=0

20.88-12(dx/dt)=0

dx/dt=1.74

the quantity supplied changing is 1.74 hundred units with respect to time

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