:
y`x= = =
2- .
35. :,,,.
f (x) [a;b] () .
f '(c),
f '(c)=0.
36. .
.. .. ->x0= ->x0 , .
,f(x),g(x).f`(x),g`(x)- . 0, g`(x0)
f(x) g(x) . 0,
f`(x) g`(x) . 0
!
, ..
37. . .( -)
1. -, . -.
1: y=f(x) [a,b],:
1)f`(x)<0,x
2)f`(x)>0,x y=f(x) ( .
: 2 1 2 (a,b),a<x1<x2<b, f(x)- (1,2) [x1;x2],.. (1,2) f(x2)-f(x1)=f`(c)(x2-x1)
f`(c)>0, f(x2)-f(x1)>0= f(x2)>f(x1) x2>x1(..-)
f`(c)<0= f(x2)-f(x1)<0= f(x2)<f(x1) 1<x2(..-)
0 ( )-y=f(x), . 0, . 0. f(x)<f(x0)(f(x0)>f(x0))
max min - .
2:(. . . )
.0 . -f(x), =0, . .
. =0 . 1- .
3( . . )
y=f(x) .0 f`(x0)=0,:
1) f`(x)<0,x
2) f`(x)>0,x
! , -f(x) 0, .