1y=2/3x³-4x²+3
y`=2x²-8x=2x(x-4)=0
x=0 x=4
+ _ +
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возр 0 убыв 4 возр
х∈[0;4] 0+1+2+3+4=10
4)y=2x³+3x²-12x+7
y`=6x²+6x-12=6(x²+2x-3)=0
x1=x2=-1 U x1*x2=-2⇒x1=-2 U x2=1
+ _ +
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возр 0 убыв 4 возр
x∈[-2;1] я бы поставила круглые скобки,но там нет в ответе
5)y=x²-10x+3
y`=2x-10=0
x=5∈[1;7]
y(1)=1-10+3=-6-max
y(5)=25-50+3=-22 min
y(7)=49-70+3=-18
6)y=x²-6x+4
y`=2x-6=0
x=3∈[0;3]
y(0)=4-max
y(3)=9-18+4=-5 min
7)y=x²+10x+3
y`=2x+10=0
x=-5∈[-9;-5]
y(-9)=81-90+3=-6 max
y(-5)=25-50+3=-22 min
8)y=x³-6x²+1
y`=3x²-12x=3x(x-4)=0
x=0∈[-2;8]
x=4∈[-2;8]
y(-2)=-8-24+1=-31min
y(0)=1
y(4)=64-96+1=-31min
y(8)=512-384+1=129 max
9)f(x)=sin2x+2cosx
f`(x)=2cos2x-2sinx=2-4sin²x-2sinx=0
sinx=a
-2(2a²+a-1)=0
D=1+8=9
a1=(-1-3)/4=-1⇒sinx=-1x=-π/2∉[π/2;π]
a2=(-1+3)/4=1/2⇒sinx=1/2⇒x=π/6∉[π/2;π]
f(π/2)=sinπ+2cosπ/2=0+0=0
f(π)=sin2π+2cosπ=0-2=-2 min
10)y=x²-2x-1
y`=2x-2=0
x=1∈[-1;1]
y(-1)=1+2-1=2 max
y(1)=1-2-1=-2
11)y=4x²+1/x
y`=8x-1/x²=(8x³-1)/x²=0
8x³-1=0⇒8x³=1⇒x³=1/8⇒x=1/2∈[1/4;1]
y(1/4)=1/4+4 = 4 1/4
y(1/2)=1+2=3
y(1)=4+1=5
3+5=8
12)y=2x³+3x²-12x
y`=6x²+6x-12=6(x²+x-2)=0
x1+x2=-1 U x1*x2=-3
x1=-2∉[0;2]
x2=1∈[0;2]
y(0)=0
y(1)=2+3-12=-7min
y(2)=16+12-24=4