函數(shù)Y=X/(X+3) X屬于(2分之根號2,三倍根號20)最小值是?

熱心網(wǎng)友

y=x/(x+3)=[(x+3)-3]/(x+3)=1-3/(x+3),3/(x+3)在x∈[√2/2,3√20]上為減函數(shù) 故y=1-3/(x+3)在此區(qū)間上為增函數(shù),故在x=√2/2時函數(shù)取最小值y=1-3/(√2/2+3)=1-6/(6+√2),分母有理化并化簡可得y=(-1-3√2)/17

熱心網(wǎng)友

[(根號3) - 1] / 2 你應(yīng)該看得懂吧

熱心網(wǎng)友

區(qū)間至少應(yīng)該左閉吧 易知函數(shù)在該區(qū)間上是增函數(shù) 所以當(dāng)X=2分之根號2時,有最小值.代入即可. 如果區(qū)間是開的話,則該函數(shù)在該區(qū)間上無最小值.