※ 引述《bbb286bp6 (bbb286bp6)》之銘言：
: 6.A manufacturer of digital clocks determines that he can sell x clocks per
: week at price p where x and p are related by the equation
: x^2+3xp+p^2=4400.
: This equation determines demand as a function of price,x=Q(p), near the
: point (p.,x.)=(40,20) ---("."為下標0)
: (a) If price is increasing at the rate of 50% per week how fast is demand
: changing when p=$40?
: (b) Find dx/dp at the point (p.,x.)=(40,20)
(a) 令p=at => dp/dt= a = 0.5 (依題目敘述)
2 2 2 2 2
x +3xp+p = 4400 => x +3xat+a t = 4400 (將a帶入和對t微分)
=> 2x(dx/dt) + 3/2t(dx/dt) + 3/2x + 1/2t = 0
=> dx/dt = (3/2x+1/2t) / (-2x-3/2t)
=> = (3/2x+ p ) / (-2x-3p ) 帶入(p,x)=(40,20)
=> = - 7/16 #
2 2
(b) x +3xp +p =4400 => 2x(dx/dp) + 3p(dx/dp) + 3x + 2p = 0
=> dx/dp = - (3x+2p)/(2x+3p) 帶入(40,20)
= - 7/8 #
(有錯請不吝指正)
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