⑩天掌 Teaching Plan on Advanced Mathematics 证yx1,x2∈(ab,且x1<x2,应用拉氏定理得 f(x2)-f(x1)=∫(5)(x2-x1)(x1<5<x2) x,>0 若在(an,b内,∫(x)>0,则f(2)>0, ∴∫(x2)>∫(x1) y=f(x)在a,b上单调增加 若在(a,呐内,f(x)<0,则∫()<0 f∫(x2)<∫(x1) y=f(x)在a,b上单调减少 2004-4-10Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 证 , ( , ),  x1 x2  a b , 且 x1  x2 应用拉氏定理,得 ( ) ( ) ( )( ) ( ) 2 1 x2 x1 x1 x2 f x − f x = f   −    0,  x2 − x1  若在(a,b)内，f (x)  0, 则 f ( )  0, ( ) ( ). 2 x1  f x  f  y = f (x)在[a,b]上单调增加. 若在(a,b)内，f (x)  0, 则 f ( )  0, ( ) ( ). 2 x1  f x  f  y = f (x)在[a,b]上单调减少. 2004-4-10