★ 设函数f(x) = [ (sinθ / 3) * x^3 ] + [ ((√3)cosθ / 2) * x^2 ] + tanθ (.)

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★ 设函数f(x) = [ (sinθ / 3) * x^3 ] + [ ((√3)cosθ / 2) * x^2 ] + tanθ (.)

★ 设函数f(x) = [ (sinθ / 3) * x^3 ] + [ ((√3)cosθ / 2) * x^2 ] + tanθ (.)
★ 设函数f(x) = [ (sinθ / 3) * x^3 ] + [ ((√3)cosθ / 2) * x^2 ] + tanθ (.)

★ 设函数f(x) = [ (sinθ / 3) * x^3 ] + [ ((√3)cosθ / 2) * x^2 ] + tanθ (.)
f'（x）=sinθx²+√3cosθx
f'（1）=sinθ+√3cosθ=（1/2）×sin（θ+π/6）
θ∈[0,5π/12],则θ+π/6∈[π/6,7π/12].
∴θ+π/6=π/2,即θ=π/3时,f'（1）有最大值1/2.
θ+π/6=π/6,即θ=0时,f'（1）有最小值0.
综上,f'（1）的取值范围是[0,1/2].

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