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[ 東京工業大学 1960 年 数学Ⅲ ２ ]

a≦ ≦x b (ab) で f x( )0 のとき， 1 2

( ) , ( ) ( ) ( )

b b

a a

N f x dx v t x t f x dx

N とおく。

( )

v t を最小にするtの値をM とする。

(1) M を求めよ。

(2) v t( )v M( ) (t M)2 であることを示せ。

参照

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