1.当x∈[a,b]时,f'(x)>0,则f(x)在区间[a,b]上是增加的;当x∈[a,b]时,f'(x)<0,则f(x)在区间[a,b]上是减少的. 2.若f(x)在区间[a,b]上是增加的,则f'(x)≥0在[a,b]上恒成立(f'(x)不恒为0);若f(x)在区间[a,b]上是减少的,则f'(x)≤0在[a,b]上恒成立(f'(x)不恒为0). 3.若f(x)在[a,b]上是增加的,则当x∈[a,b]时,有f(a)≤f(x)≤f(b).