证明函数f(x)=x²+16/x²(x>0)在区间(0,2)递减
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证明函数f(x)=x²+16/x²(x>0)在区间(0,2)递减
证明函数f(x)=x²+16/x²(x>0)在区间(0,2)递减
证明函数f(x)=x²+16/x²(x>0)在区间(0,2)递减
证明:设x²=t,则f(t)=t+16/t
∵x>0
∴t∈(-∞,0)U(0,+∞)
∵f(t)在t∈(0,√16)上递减
∴f(x)在x²∈(0,4)上递减
∴f(x)在x∈(-2,0)和(0,2)递减