(a) as small as possible.
(b) as large as possible.
Find a number in the closed interval [5/6, 7/6] such that the sum of the number and its reciprocal is?
2015-12-09 1:07 pm
回答 (2)
2015-12-09 2:05 pm
S = x+1/x , where 5/6 < x < 7/6
dS/dx = 1 -1/x^2 = 0
1= 1/x^2
x^2 = 1
x = 1
d^2S/dx^2 = d/dx ( 1-1/x^2) = d/dx ( -x^(-2) ) = (-1)(-2) x^(-3) = 2/x^3 > 0 if 5/6 < x < 7/6
x = 1
The number is 1 and the sum of the number and its reciprocal can only be minimized.
5/6 < 1 < 7/6
dS/dx = 1 -1/x^2 = 0
1= 1/x^2
x^2 = 1
x = 1
d^2S/dx^2 = d/dx ( 1-1/x^2) = d/dx ( -x^(-2) ) = (-1)(-2) x^(-3) = 2/x^3 > 0 if 5/6 < x < 7/6
x = 1
The number is 1 and the sum of the number and its reciprocal can only be minimized.
5/6 < 1 < 7/6
2015-12-09 1:11 pm
y = x/6 + 6/x = x^2/(6x) + 36/(6x) = (x^2 + 36)/(6x)
收錄日期: 2021-04-21 15:39:57
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