f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3...f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3+2/3后就算
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![f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3...f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3+2/3后就算](/uploads/image/z/12588818-50-8.jpg?t=f%28x%29%3Dlnx-1%2Fx%2Cx%E2%89%A52%2C%E8%AF%81%E6%98%8E%EF%BC%9Af%EF%BC%88x%EF%BC%8D1%EF%BC%89%E2%89%A42x%EF%BC%8D5%2C%E6%88%91%E7%AE%97%E5%88%B0h%EF%BC%88x%EF%BC%89%3Dln%EF%BC%88x%EF%BC%8B1%EF%BC%89%EF%BC%8D1%2F%EF%BC%88x%EF%BC%8B1%EF%BC%89%EF%BC%8D2x%EF%BC%8B5%E2%89%A4h%282%29%3Dln3...f%28x%29%3Dlnx-1%2Fx%2Cx%E2%89%A52%2C%E8%AF%81%E6%98%8E%EF%BC%9Af%EF%BC%88x%EF%BC%8D1%EF%BC%89%E2%89%A42x%EF%BC%8D5%2C%E6%88%91%E7%AE%97%E5%88%B0h%EF%BC%88x%EF%BC%89%3Dln%EF%BC%88x%EF%BC%8B1%EF%BC%89%EF%BC%8D1%2F%EF%BC%88x%EF%BC%8B1%EF%BC%89%EF%BC%8D2x%EF%BC%8B5%E2%89%A4h%282%29%3Dln3%2B2%2F3%E5%90%8E%E5%B0%B1%E7%AE%97)
f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3...f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3+2/3后就算
f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3...
f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3+2/3后就算不下去了
f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3...f(x)=lnx-1/x,x≥2,证明:f(x-1)≤2x-5,我算到h(x)=ln(x+1)-1/(x+1)-2x+5≤h(2)=ln3+2/3后就算
证:f(x-1)=ln(x-1)-1/(x-1)
f(x-1)-2x+5=ln(x-1)-1/(x-1)-2(x-1)+3=lnt-1/t-2t+3(t=x+1,t≥1)
设g(t)=lnt-1/t-2t+3(t≥1),g'(t)=1/t+1/t^2-2在t≥1时恒小于0,g(t)单调递减
g(t)≤g(t)max=g(1)=0
即f(x-1)≤2x-5
h(t)=lnt-1/t-2(t+1)+5=lnt-1/t-2t+3
其中 t=x-1,t≥1
h'(t)=1/t+1/t^2-2=(1/t+1/2)^2-1/4-2≤(1/1+1/2)^2-9/4=0
得解
h(t)=lnt-1/t-2(t+1)+5=lnt-1/t-2t+3
其中 t=x-1,t≥1
h'(t)=1/t+1/t^2-2=(1/t+1/2)^2-1/4-2≤(1/1+1/2)^2-9/4=0