F(x)=x^4-8x²+3,[-1;2]
f`(x)=4x³-16x²=4x(x²-4)=4x(x-2)(x+2)=0
x=0∈[-1;2],x=2∈[-1;2],x=-2∉[-1;2]
f(-1)=1-8+3=-4
f(0)=3 наиб
f(2)=16-32+3=-13 наим
f(x)=x³+9x²+15x,[-3;-2]
f`(x)=3x²+18x+15=0
x²+6x+5=0
x1+x2=-6 U x1*x2=5
x1=-5∉[-3;-2],x2=-1∉[-3;-2]
f(-3)=-27+81-45=9 наиб
f(-2)=-8+36-30=-2 наим
f(x)=x-√x,[0;4]
f`(x)=1-1/2√x=(2√x-1)/2√x=0
2√x=1⇒√x=1/2⇒x=1/4∈[0;4]
f(0)=0-0=0
f(1/4)=1/4-1/2=-1/4 наим
f(4)=4-2=2 наиб
f(x)=2cosx-cos2x,[0;π]
f`(x)=-2sinx+2sin2x=0
-2sinx+4sinxcosx=0
-2sinx(1-2cosx)=0
sinx=0⇒x=πn,n∈z
x=0∈[0;π]
x=π∈[0;π]
cosx=1/2⇒x=+-π/3+2πn
x=π/3∈[0;π]
f(0)=2cos0-cos0=2*1-1=1
f(π/3)=2cosπ/3-cos2π/3=2*1/2+1/2=1,5наиб
f(π)=2cosπ-cos2π=2*(-1)-1=-3 наим