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謝謝老師
二次函數極值一問
版主: thepiano
Re: 二次函數極值一問
第 1 題
1 + 1 + 1 + ...... + 1 + 1 + 1
2 + 2 + 2 + ...... + 2 + 2
3 + 3 + 3 + ...... + 3
:
:
(n-1) + (n-1)
n
從後面看回來,而且要看直行
第 2 題
2 - √2 (約 0.586) ≦ f(x) ≦ 2 + √2 (約 3.414)
以下 log 均以 2 為底
-1 < logf(x) < 2
logf(x) = 0,f(x) = 1,x = -1
logf(x) = 1,f(x) = 2,x = 1 - √2 or 1 + √2
故
(1) x < -1,[logf(x)] = -1,[logf(x)] + 2 = 1
(2) -1 ≦ x < 1 - √2,[logf(x)] = 0,[logf(x)] + 2 = 2
(3) 1 - √2 ≦ x ≦ 1 + √2,[logf(x)] = 1,[logf(x)] + 2 = 3
(4) 1 + √2 < x,[logf(x)] = 0,[logf(x)] + 2 = 2
1 + 1 + 1 + ...... + 1 + 1 + 1
2 + 2 + 2 + ...... + 2 + 2
3 + 3 + 3 + ...... + 3
:
:
(n-1) + (n-1)
n
從後面看回來,而且要看直行
第 2 題
2 - √2 (約 0.586) ≦ f(x) ≦ 2 + √2 (約 3.414)
以下 log 均以 2 為底
-1 < logf(x) < 2
logf(x) = 0,f(x) = 1,x = -1
logf(x) = 1,f(x) = 2,x = 1 - √2 or 1 + √2
故
(1) x < -1,[logf(x)] = -1,[logf(x)] + 2 = 1
(2) -1 ≦ x < 1 - √2,[logf(x)] = 0,[logf(x)] + 2 = 2
(3) 1 - √2 ≦ x ≦ 1 + √2,[logf(x)] = 1,[logf(x)] + 2 = 3
(4) 1 + √2 < x,[logf(x)] = 0,[logf(x)] + 2 = 2