函数f(x)=ax²+1/bx(b>0)(1)求证f(x)的单调区间.(2)a>0,x1+x2>0,x2+x3>0,x1+x3>0
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![函数f(x)=ax²+1/bx(b>0)(1)求证f(x)的单调区间.(2)a>0,x1+x2>0,x2+x3>0,x1+x3>0](/uploads/image/z/9448581-21-1.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3Dax%26%23178%3B%2B1%2Fbx%28b%3E0%29%281%29%E6%B1%82%E8%AF%81f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4.%282%29a%3E0%2Cx1%2Bx2%3E0%2Cx2%2Bx3%3E0%2Cx1%2Bx3%3E0)
函数f(x)=ax²+1/bx(b>0)(1)求证f(x)的单调区间.(2)a>0,x1+x2>0,x2+x3>0,x1+x3>0
函数f(x)=ax²+1/bx(b>0)(1)求证f(x)的单调区间.(2)a>0,x1+x2>0,x2+x3>0,x1+x3>0
函数f(x)=ax²+1/bx(b>0)(1)求证f(x)的单调区间.(2)a>0,x1+x2>0,x2+x3>0,x1+x3>0
定义域为x不等于0
对f(x)求导,得
f'(x)=2ax-1/bx^2
令f'(x)>0,得2ax-1/bx^2>0
因为b>0,则2abx>1/x^2
则2abx^30,则x^30 时单增区间为x