# Задачи на нахождение наибольшего и наименьшего значений функции на отрезке

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. :. = (5) 2. y = I x I. y = os 2 x. y = -2 sin 3 x. = log 2 ( x 3 -5). y = I x 2 -2 x I. y`=1 >0 y` =0 y`= -1

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• : = (5)2 ` = 50x = log2 (x3-5) y = -2sin 3x y` = -6os3x y = os2x y`= -sin 2x y = IxI y`=1 >0y` =0y`= -1
• :D(y) = (-; 2) y = - x2+ 4x D(y) = (-;+) y = sin 2x D(y)= Ry = ln (3x2+1) D(y)= Ry = tg x y = log (x-8) (x-1) D(y)= (8;9) U (9; +) y = lg IxI; D(y) = (-; 0) U (0; +) D(y)= (-;-4] U [ 4; +)y = ln (5 x2)

• :y = 25x+6 E(y) = (0; +)y = 3sin 2x; E(y) = [-3;3]y = -4 cos6x 9 E(y) = [-13; -5] E(y) = (-;+)y = Ix+1I E(y) = [0;+) E(y) = [0;3]

• f(x)- ,

,

• y=f(x) [a; b]yyab------------------------------------------------------------------------y=f(x) [a; b]y= f(a)

y= f(b)------------------------------------------------------

• y=f(x) [a; b]--------------------------------------------------------------------------yyaby=f(x) [a; b]

y=f(b)

y=f(a)----------------------------------------------------

• y=f(x) [a; b]----------------------------------------------------------------------------------------baXmaxyyy=f(x) [a; b] max [a; b]

y = y(max)

y =y(a)-----------------------------------------

• y=f(x) [a; b]yyba-------------------------Xmax------------------------------------------------------------------------y=f(x) [a; b] max [a; b]

y = y(max)

y =y(b)-----------------------------------------------

• y=f(x) [a; b]y----------------------------ab--------------------------y-----Xminy=f(x) [a; b] min [a; b]

y = y(min)

y =y(a)---------------------------------------------

• y=f(x) [a; b]yybaXmin---------------------------------------------------------------------------------------------------------y=f(x) [a; b] min [a; b]

y = y(min)

y =y(b)----------------------------------------------------

• y=f(x) [a; b]---------------------------------------------------------------------XmaxXmin--------------------------------ab----------yyy=f(x) [a; b]

y = y(min)

y = y(max)

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• ( )

• () [0;1] [1;4]

• [0;3]

• ABCD , 2, AD BC, , AB , , C D CD y=x3-5x2-1 [-1;3]

• *