2015考研数学基础班讲义－微积分第四讲.pdf

2008 B 609 y f (x ) x 0 y f (x ) x x0 x x0 ∆f (x ) f (x +∆x) −f (x ) x 0 0 0 0 x y f (x ) x N (x ,δ) 0 0 0 x f (x ) x0 x0 N (x0 ,δ) f (x) ≤f (x ) ∆f f (x) −f (x ) ≤0 N (x ,δ) x f (x ) 0 0 0 0 ∆f f (x +∆x) −f (x ) x x0 0 0 ≤0 ∆x x −x 0 f ∆ lim ≤0 f ′(x ) ≤0 + 0 ∆x →0+ ∆x ∆f f (x) −f (x ) ∆f x x0 0 ≥0 lim ≥0 f ′(x ) ≥0 − 0 ∆x x −x ∆x →0− ∆x 0 f ′(x0 ) ≥0 f ′(x0 ) ≤0 f ′(x0 ) 0 f (x ) °N (x ,δ) ∀x ∈N (x ,δ) f (x) ≤f (x ) 0 0 0 ≥f (x )) °x f ′(x ) 0 0 0 0 y f (x ) [a,b] f +′(a)f −′(b) 0 1 2008 B 609 ∃x0 ∈(a,b) f ′(x0 ) 0 x 0 ′ f ′(a) 0 x a f (x ) a, b + f (x ) x f (x ) f (a) f (a) f (x