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3fx-f(1/x)=1/x求fx的极值
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3fx-f(1/x)=1/x求fx的极值
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答案和解析
3f(x)-f(1/x)=1/x (1)
let y= 1/x
3f(1/y)-f(y)=y
3f(1/x)-f(x)=x (2)
(2)+3(1)
8f(x) =x + 3/x
f(x) = (1/8)( x+ 3/x)
f'(x) = (1/8)( 1- 3/x^2) =0
x^2-3 =0
x=√3 (max )or -√3 (min)
max f(x)
= f(√3)
=(1/8)(√3 + 3/√3)
=√3/4
min f(x)
= f(-√3)
=(1/8)(-√3 + -3/√3)
=-√3/4
let y= 1/x
3f(1/y)-f(y)=y
3f(1/x)-f(x)=x (2)
(2)+3(1)
8f(x) =x + 3/x
f(x) = (1/8)( x+ 3/x)
f'(x) = (1/8)( 1- 3/x^2) =0
x^2-3 =0
x=√3 (max )or -√3 (min)
max f(x)
= f(√3)
=(1/8)(√3 + 3/√3)
=√3/4
min f(x)
= f(-√3)
=(1/8)(-√3 + -3/√3)
=-√3/4
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