f(x) 0 , : .
. u = φ(x) x, y = f (u) u = φ(x), y = f (φ(x)) x, : .
( ). f (x) g (x) , , g ¢(x) f (a) = g (a) = 0 ( ), , ( ) :
.
( ).
1. f (x) (a, b) f ¢(x) > 0 x (a, b), (a, b).
2. f (x) (a, b) f ¢(x) < 0 x (a, b), (a, b).
y = f (x), δ - , f (x) < f ().
y = f (x), δ - , f (x) > f ().
.
.
.
.
( ).
f (x) , .
, .
( ).
1. f (x) (a, b), , (, , ). f ¢(x) , f (x) , , f (x) .
2. f ¢() = 0 f ¢¢() . , f ¢¢() < 0, , f ¢¢() > 0, .
y = f (x) (a, b), .
y = f (x) (a, b), .
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( () ). (a, b) f (x) , y = f (x) . (a, b) f (x) , y = f (x) .
, , .
( ). f ¢¢(x) , , , .
, .
x = a y = f (x), .
y = b y = f (x), .
y = kx + b y=f (x), :
()
b = (b = .