y = f(x) is an decreasing in interval [0, a] . Futhermore, f(x) > 0
for 0 <= x < a and f(a) = 0. Prove that x‧f(x) obtains its absolute
maximum for 0 <= x <= a if and only if (y / x)‧(dx / dy) = -1
y = f(x) 在區間 [0, a] 上遞減，而且對於 0 <= x < a，f(x) > 0
以及 f(a) = 0。證明 x‧f(x) 的值為絕對極大當且僅當
(y / x)‧(dx / dy) = -1
Absolute maximum
2008-03-01 7:00 pm
回答 (1)
2008-03-03 12:28 am
✔ 最佳答案
if g(x,y) = x‧f(x) = x*y 發生極值 g/dx dy = 0 (發生極值處 在 微分為0的地方)
g/dx dy = xdy + ydx = 0
xdy + ydx = 0
-> xdy = ydx
-> (y / x)‧(dx / dy) = -1
所以 (y / x)‧(dx / dy) = -1 時 x‧f(x) 的值為絕對極大
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