Y'=(√(9+cos²x))'=[1/2√(9+cos²x)²]*(9+cos²x)=2cosx*(cosx)'/2(9+cos²x)=2cosx*(-sinx)/(2(9+cos²x))=-sinxcosx/(9+cos²x)=-(1/2)sin2x/(9+cos²x)
y'=0
-(1/2)sin2x/(9+cos²x)=0
-(1/2)sin2x=0, 9+cos²x≠0
sin2x=0
2x=πn, n∈Z
x=πn/2, n∈Z
π/3≤πn/2≤2π/3
1/3≤n/2≤2/3 |*6
2≤3n≤4
2/3≤n≤4/3
n=1
x=π/2
y(π/3)=√(9+cos²(π/3))=√(9+1/4)=√9,25
y(2π/3)=√(9+cos²(2π/3))=√(9+1/4)=√9,25
y(π/2)=√(9+cos²(π/2))=√(9+0)=√9
у наим. =у(π/2)=3