∵x∈[5π/4,35π/12]
∴2/5x∈[1/2π,7/6π]
∴2/5x-π/6∈[1/3π,π]
∴sin(2/5x-π/6)∈[0,1]
当sin(2/5x-π/6)=1
2/5x-π/6=½π
x=5/3π…………………………(i)
当sin(2/5x-π/6)=0
2/5x-π/6=π
x=35/12π………………………(ii)
综上(i)(ii)得
f(x)max=1,x=5/3π
f(x)min=0,x=35/12π