Y`=(√(24+sin²x))` [-π/6;5π/6]
y`=sinx*cosx/√(24+sinx)=0
sinx*cosx=0
sinx=0
x=πn
π/6<πn<5π/6<br>1/6cosx=0
x=π/2+πn
π/6<π/2+πn<5π/6<br>1/6<1/2+n<5/6<br>-2/3n=0 ⇒x=π/2
y(π/2)=√(24+sin²(π/2))=√25=5
y(π/6)=√(25+sin²(π/6))=√25,25
y(5π/6)=√(25+sin²(5π/6))=√25,25
ymax=√25,25.