作业帮f(x)在[a,b]上连续,在(a,b) 内可导,且 f '(x)≤0,F(x)=1/(x-a)∫(x-a)f(t)dt,证明在(a,b) 内 F'(x)≤0.由题意有F'(x)=[f(x)(x-a)-∫(x-a)f(t)dt]/(x-a)^2,x∈(a,b)
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![f(x)在[a,b]上连续,在(a,b) 内可导,且 f '(x)≤0,F(x)=1/(x-a)∫(x-a)f(t)dt,证明在(a,b) 内 F'(x)≤0.由题意有F'(x)=[f(x)(x-a)-∫(x-a)f(t)dt]/(x-a)^2,x∈(a,b)](/uploads/image/z/8820890-26-0.jpg?t=f%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+f+%27%28x%29%E2%89%A40%2CF%28x%29%3D1%2F%28x-a%29%E2%88%AB%28x-a%29f%28t%29dt%2C%E8%AF%81%E6%98%8E%E5%9C%A8%28a%2Cb%29+%E5%86%85+F%27%28x%29%E2%89%A40.%E7%94%B1%E9%A2%98%E6%84%8F%E6%9C%89F%27%28x%29%3D%5Bf%28x%29%28x-a%29-%E2%88%AB%28x-a%29f%28t%29dt%5D%2F%28x-a%29%5E2%2Cx%E2%88%88%28a%2Cb%29)
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f(x)在[a,b]上连续,在(a,b) 内可导,且 f '(x)≤0,F(x)=1/(x-a)∫(x-a)f(t)dt,证明在(a,b) 内 F'(x)≤0.由题意有F'(x)=[f(x)(x-a)-∫(x-a)f(t)dt]/(x-a)^2,x∈(a,b)
f(x)在[a,b]上连续,在(a,b) 内可导,且 f '(x)≤0,F(x)=1/(x-a)∫(x-a)f(t)dt,证明在(a,b) 内 F'(x)≤0.
由题意有F'(x)=[f(x)(x-a)-∫(x-a)f(t)dt]/(x-a)^2,x∈(a,b)
f(x)在[a,b]上连续,在(a,b) 内可导,且 f '(x)≤0,F(x)=1/(x-a)∫(x-a)f(t)dt,证明在(a,b) 内 F'(x)≤0.由题意有F'(x)=[f(x)(x-a)-∫(x-a)f(t)dt]/(x-a)^2,x∈(a,b)
φ‘(x)=(f’(x)(x-a)-f(x))/(x-a)^2,a
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