函数fx=2cos的平方x+3sinx+3,［x∈π/6.2π/3］的值域

Question

函数fx=2cos的平方x+3sinx+3,［x∈π/6.2π/3］的值域

Answer 1

f(x)=2[1-(sinx)^2]+3sinx+3 =-2(sinx)^2+3sinx+5 因为x∈[π/6,2π/3] 所以1/2≤sinx≤1 所以值域为[6,49/8]