设f(x)可导,F(x)=f(x)(1+|sinx|),若F(X)在点x=0处可导,则必有(?)A,f(0)=0B,f'(0)=0C,f(0)+f'(0)=0D,f(0)-f'(0)=0谢谢各位了,把过程也写清楚点我追加分!
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![设f(x)可导,F(x)=f(x)(1+|sinx|),若F(X)在点x=0处可导,则必有(?)A,f(0)=0B,f'(0)=0C,f(0)+f'(0)=0D,f(0)-f'(0)=0谢谢各位了,把过程也写清楚点我追加分!](/uploads/image/z/10263009-57-9.jpg?t=%E8%AE%BEf%28x%29%E5%8F%AF%E5%AF%BC%2CF%EF%BC%88x%EF%BC%89%3Df%28x%29%281%2B%7Csinx%7C%29%2C%E8%8B%A5F%EF%BC%88X%EF%BC%89%E5%9C%A8%E7%82%B9x%3D0%E5%A4%84%E5%8F%AF%E5%AF%BC%2C%E5%88%99%E5%BF%85%E6%9C%89%EF%BC%88%3F%EF%BC%89A%2Cf%280%29%3D0B%2Cf%27%280%29%3D0C%2Cf%280%29%2Bf%27%280%29%3D0D%2Cf%280%29-f%27%280%29%3D0%E8%B0%A2%E8%B0%A2%E5%90%84%E4%BD%8D%E4%BA%86%2C%E6%8A%8A%E8%BF%87%E7%A8%8B%E4%B9%9F%E5%86%99%E6%B8%85%E6%A5%9A%E7%82%B9%E6%88%91%E8%BF%BD%E5%8A%A0%E5%88%86%21)
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设f(x)可导,F(x)=f(x)(1+|sinx|),若F(X)在点x=0处可导,则必有(?)A,f(0)=0B,f'(0)=0C,f(0)+f'(0)=0D,f(0)-f'(0)=0谢谢各位了,把过程也写清楚点我追加分!
设f(x)可导,F(x)=f(x)(1+|sinx|),若F(X)在点x=0处可导,则必有(?)
A,f(0)=0
B,f'(0)=0
C,f(0)+f'(0)=0
D,f(0)-f'(0)=0
谢谢各位了,把过程也写清楚点我追加分!
设f(x)可导,F(x)=f(x)(1+|sinx|),若F(X)在点x=0处可导,则必有(?)A,f(0)=0B,f'(0)=0C,f(0)+f'(0)=0D,f(0)-f'(0)=0谢谢各位了,把过程也写清楚点我追加分!
在0附近
xo时F(x)=f(x)(1+sinx)
x0时F'(x)=f'(x)+f'(x)sinx+f(x)sin'x [2]
因为F(x)在 x=0处可导
所以 x趋向于0-时于趋向于0+时 F'(0)- = F'(0)+
所以X=0时 【1】式=【2】式
所以f'(0)-f'(0)sin0-f(0)sin'0 =f'(0)+f'(0)sin0+f(0)sin'0
整理 知f(0)=0
选A
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