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發表於 2010-2-24 22:42:21
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=.=咁似延數的,不過好似仲有幾課先幫到你...而且唔識英文....=.=好似講左好多廢話
vbnn20 發表於 2010-2-24 09:57 PM
果d p maths黎.
本帥打救你
a)
f'(x )=1/4x^(-3/4)-1/4 =1/4[1/(x^3/4) -1] f'(x ) = 0 for x=1 <0 for 1<x<inf. >0 for 0<x <1 therefore, f(x ) attains its max at x=1 for all x?(0,inf.) because f is cont. on [0,inf.) , => f(x ) <= f(1 ) x^1/4 - 1/4x -3/4 <=0
replace x by x/y >=0 (x/y)^1/4 <= 1/4(x/y)-3/4 x^1/4 * y^3/4 <= 1/4x -3/4y
b)
since F and G are non-negative, i.e. F(x ) >=0 and G(x )>=0 by a, sub x=F(x ) , Y= G(x ) [F(x )]^1/4 *[G(x )]^3/4 <= 1/4 F(x ) +3/4G(x ) in(a->b) [F(x )]^1/4 *[G(x )]^3/4 dx <= in(a->b) 1/4 F(x ) +3/4G(x ) dx =1/4*1+3/4*1 =1/4+3/4=1 |
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