已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f(x)f'(x)+f^2(x)的值域是求当x属于【0,π/2】
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![已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f(x)f'(x)+f^2(x)的值域是求当x属于【0,π/2】](/uploads/image/z/616365-45-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsinx%2Bcosx%2Cf%27%28x%29%E6%98%AFf%28x%29%E7%9A%84%E5%AF%BC%E5%87%BD%E6%95%B0.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsinx%2Bcosx%2Cf%27%28x%29%E6%98%AFf%28x%29%E7%9A%84%E5%AF%BC%E5%87%BD%E6%95%B0%2C%E6%B1%82f%27%28x%29%E5%8F%8Ay-f%27%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%2C%E6%B1%82%E5%BD%93x%E5%B1%9E%E4%BA%8E%E3%80%900%2C%CF%80%E3%80%812%E3%80%91%2CF%28x%29%3Df%EF%BC%88x%29f%27%28x%29%2Bf%5E2%28x%29%E7%9A%84%E5%80%BC%E5%9F%9F%E6%98%AF%E6%B1%82%E5%BD%93x%E5%B1%9E%E4%BA%8E%E3%80%900%EF%BC%8C%CF%80%2F2%E3%80%91)
已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f(x)f'(x)+f^2(x)的值域是求当x属于【0,π/2】
已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.
已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f(x)f'(x)+f^2(x)的值域
是求当x属于【0,π/2】
已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数.已知函数f(x)=sinx+cosx,f'(x)是f(x)的导函数,求f'(x)及y-f'(x)的最小正周期,求当x属于【0,π、2】,F(x)=f(x)f'(x)+f^2(x)的值域是求当x属于【0,π/2】
f(x) = sinx+cosx
f'(x) = cosx -sinx
= √2((1/√2)cosx - (1/√2)sinx)
= √2(cos(x+π/4))
f'(x) 的最小正周期 = 2π
y-f'(x)
=sinx+cosx -(cosx-sinx)
=2sinx
y-f'(x) 的最小正周期 = 2π
F(x)= f(x)f'(x)+[f(x)]^2
=(sinx+cosx)(cosx-sinx)+ (cosx-sinx)^2
= (cosx)^2 - (sinx)^2 + 1-2sinxcosx
= cos2x - sin2x +1
= √2((1/√2)cos2x-(1/√2)sin2x) +1
=√2(cos(2x+π/4)+1
F(x)=f(x)f'(x)+f^2(x)的值域 = [1-√2,2]
f'(x)=cosx- sinx 最小正周期为2π
y-f'(x) =2sinx 最小正周期为2π
F(x)=f(x)f'(x)+f^2(x) =cos2x +sin2x +1
=根号2* sin(2x+π/4) +1 x∈[0, π/2], 2x+π/4 ∈[π/4, 5π/4]
F(x)的值域为[0, 1+根号2]