Question

已知函数f(x)=x^2+2xtana-1,x属于[-1,根号3],其中a属于(-π/2,π/2)

Answer 1

(1)当θ=-π/6时,tanθ=-√3/3

f(x)=x^2-2√3x/3-1=(x-√3/3)^2-4/3

f(x)在[-1,√3/3]单调减,在[√3/3,√3]单调增

f(-1)=1+2√3/3-1=2√3/3

f(√3)=0

所以f(x)在x=-1处取得最大2√3/3

在x=√3/3处取得最小-4/3

(2)f(x)=x^2+2xtanθ-1=(x+tanθ)^2-1-(tanθ)^2

当-tanθ≤-1即tanθ≥1,即π/4≤θ