[中學] 求倒數和的最大最小值

[SmallLuLu (小嚕嚕)]

1<=t<=9

求t+9/t最大值最小值

最小值用算幾不等式可求出當t=3有最小值6

那最大值呢?

t不管帶1或9都有最大值10

但是以高中數學來看

要怎樣做出合理的解釋呢?

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→ CaptainH    :1<=t<=9 => (t-1)(t-9)<=0, t^2-10t+9<=0
→ CaptainH    :t+9/t = (t^2+9)/t <= 10
→ CaptainH    :等號成立時 (t-1)(t-9)=0 , t=1 or 9