设函数f(x)在[a,b]上连续,在(a,b)内可导,且满足f(a)=0,若f'(x)单调增加,则φ(x)=f(x)/(x-a)也在(a,b)内单调增加.证明题
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![设函数f(x)在[a,b]上连续,在(a,b)内可导,且满足f(a)=0,若f'(x)单调增加,则φ(x)=f(x)/(x-a)也在(a,b)内单调增加.证明题](/uploads/image/z/14758675-43-5.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%28a%2Cb%29%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94%E6%BB%A1%E8%B6%B3f%28a%29%3D0%2C%E8%8B%A5f%27%28x%29%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8A%A0%2C%E5%88%99%CF%86%28x%29%3Df%28x%29%2F%28x-a%29%E4%B9%9F%E5%9C%A8%28a%2Cb%29%E5%86%85%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8A%A0.%E8%AF%81%E6%98%8E%E9%A2%98)
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设函数f(x)在[a,b]上连续,在(a,b)内可导,且满足f(a)=0,若f'(x)单调增加,则φ(x)=f(x)/(x-a)也在(a,b)内单调增加.证明题
设函数f(x)在[a,b]上连续,在(a,b)内可导,且满足f(a)=0,若f'(x)单调增加,则φ(x)=f(x)/(x-a)也在(a,b)内单调增加.
证明题
设函数f(x)在[a,b]上连续,在(a,b)内可导,且满足f(a)=0,若f'(x)单调增加,则φ(x)=f(x)/(x-a)也在(a,b)内单调增加.证明题
φ‘(x)=(f’(x)(x-a)-f(x))/(x-a)^2,a
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