推 wyob :感謝 08/30 17:24
※ 引述《wyob (Go Dolphins)》之銘言：
: y=x^2 , y=2^x
: 想請問這兩個的交點有幾個
: 應該用均值定理嗎???
: 我只找到兩個而已
: 所以想請問一下怎麼解
: 感謝
2 x
Let f(x) ＝ x and g(x) ＝ 2 . It is okay that f,g are both in
2
Ｃ (|R). Note that if f(α) ＝ g(α) and f(β) ＝ g(β) for some α ＜ β,
then (f－g)(α) ＝ (f－g)(β) ＝ 0, by mean value theorem, there is a c in
(α,β) such that (f－g)'(c) ＝ 0. Now, since
2 x
(f－g)"(x) ＝ (㏑2) 2 － 2 ＝ 0 has only one solution, (f－g)'(x) ＝ 0 has
at most two solution, (f－g)(x) ＝ 0 has at most three solution.
Now, we know that x ＝ 2, 4 are solutions. In fact, since
1
(f－g)(-1) ＝ ── and (f－g)(0) ＝ -1, there is a solution between
2
-1 and 0. Exactly three solution.
[Supplyment Problem]
y x
Find integers x, y such that x ＝ y .
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※ 編輯: Minkowski 來自: 140.123.62.134 (08/30 17:24)