2002
y=x³-3x²+16 [1;3]
y`=3x²-6x=3x(x-2)=0
x=0∉[1;3]
x=2∈[1;3]
y` _ +
----[1]-------------[2]-------------[3]---------
y min
y(2)=8-12+19=15
2003
y=(x-16)e^(x-15) [14;16]
y`=e^(x-15)+(x-16)*e^(x-15)=e^(x-15)*(1+x-16)=(x-15)*e^(x-15)=0
x-15=0⇒x=15∈[14;15]
y` _ +
----[14]-------------[15]-------------[16]---------
y min
y(15)=(15-16)*e^(15-15)=-1
2004
y=(x-9)e^(x-8) [7;9]
y`=e^(x-8)+e^(x-8) *(x-9)=e^(x-8)*(1+x-9)=(x-8)*e^(x-8)=0
x-8=0⇒x=8∈[7;9]
y` _ +
----[7]-------------[8]-------------[9]---------
y min
y(8)=(8-9)*e^(8-8)=-1
2005
y=(x-12)e^(x-11) [10;12]
y`=e^(x-11)+e^(x-11) *(x-12)=e^(x-11)*(1+x-12)=(x-11)*e^(x-11)=0
x-11=0⇒x=11∈[10;12]
y` _ +
----[10]-------------[11]-------------[12]---------
y min
y(11)=(11-12)*e^0=-1
2006
y=(x-20)e^(x-19) [18;20]
y`=e^(x-19)+e^(x-19) *(x-20)=e^(x-19)*(1+x-20)=(x-19)*e^(x-19)=0
x-19=0⇒x=19∈[18;20]
y` _ +
----[18]-------------[19]-------------[20]---------
y min
y(19)=(19-20)*e^0=-1