f(x)=lnx.g(x)=½ax²+2x.若h(x)=f(x)-g(x)在[1,4]上单调减,求a的范围
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![f(x)=lnx.g(x)=½ax²+2x.若h(x)=f(x)-g(x)在[1,4]上单调减,求a的范围](/uploads/image/z/11967574-22-4.jpg?t=f%28x%29%3Dlnx.g%28x%29%3D%26%23189%3Bax%26%23178%3B%2B2x.%E8%8B%A5h%28x%29%3Df%28x%29-g%28x%29%E5%9C%A8%5B1%2C4%5D%E4%B8%8A%E5%8D%95%E8%B0%83%E5%87%8F%2C%E6%B1%82a%E7%9A%84%E8%8C%83%E5%9B%B4)
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f(x)=lnx.g(x)=½ax²+2x.若h(x)=f(x)-g(x)在[1,4]上单调减,求a的范围
f(x)=lnx.g(x)=½ax²+2x.若h(x)=f(x)-g(x)在[1,4]上单调
减,求a的范围
f(x)=lnx.g(x)=½ax²+2x.若h(x)=f(x)-g(x)在[1,4]上单调减,求a的范围
由题知h'(x)=1/x-ax-2≤0在【1,4】恒成立
转化为a≥1/x^2-1/2x
通过换元可解得得a≥1/2