[考古] 政大應數95年微積分(一)

[ilovecurl (ilovecurl)]

這是今年我有疑問的幾題,請高手指教

3.if f(x) is continuous on [0,1], show that there exists c in [0,1],
  such that f(c) = c.
  此題我覺得題目怪怪的,因為我只要f(x)在[0,1]間連續,有最小值大於1,那不就永遠
  找不到一個c使得f(c) = c 了?

7.In the method of Lagrange multipliers, f(x,y) is objective function.
  g(x,y) = 0 is the constraint, and (x0,y0) is the only solution.
                  Δf |
  Evaluate lim   -----|
          Δx->0  Δg |(x0,y0)
          Δy->0

9.when is f(x,y) differentiable at (a,b)?

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◆ From: 59.113.187.109
推 GayerDior:3. Bolzano定理
→ SMer:3.顯然是錯的, f(x)=2
→ SMer:7.想想使用乘數法則的先決條件
→ SMer:9.只是叫你把多變數函數可微的定義寫一次
推 ilovecurl:3.是題目錯的意思嗎?
→ SMer:Yes
→ binbinthink:9  就是多變元的可微的定義寫一下