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導(dǎo)數(shù)大題經(jīng)典(重點(diǎn)討論)練習(xí)及答案(整理、理科)-在線瀏覽

2024-09-05 05:40本頁面
  

【正文】 以函數(shù)g (x)在區(qū)間上遞增,在區(qū)間上遞減.所以函數(shù)g (x)在,或x=,所以,所以實(shí)數(shù)a的取值范圍是. (Ⅲ)因?yàn)?,令h (x)=2x2―2ax+1①顯然,當(dāng)a≤0時(shí),在(0,+∞)上h (x)>0恒成立,f (x)>0,此時(shí)函數(shù)f (x)沒有極值點(diǎn);②當(dāng)a>0時(shí),(i)當(dāng)Δ≤0,即時(shí),在(0,+∞)上h (x)≥0恒成立,這時(shí)f (x)≥0,此時(shí),函數(shù)f (x)沒有極值點(diǎn);(ii)當(dāng)Δ>0時(shí),即時(shí),易知,當(dāng)時(shí),h (x)<0,這時(shí)f (x)<0;當(dāng)或時(shí),h (x)>0,這時(shí)f (x)>0;所以,當(dāng)時(shí),是函數(shù)f (x)的極大值點(diǎn);是函數(shù)f (x)的極小值點(diǎn).綜上,當(dāng)時(shí),函數(shù)f (x)沒有極值點(diǎn);當(dāng)時(shí),是函數(shù)f (x)的極大值點(diǎn);是函數(shù)f (x)的極小值點(diǎn). 4.解:. (Ⅰ),解得. (Ⅱ). ①當(dāng)時(shí),在區(qū)間上,;在區(qū)間上,故的單調(diào)遞增區(qū)間是,單調(diào)遞減區(qū)間是. ②當(dāng)時(shí),在區(qū)間和上,;在區(qū)間上,故的單調(diào)遞增區(qū)間是和,單調(diào)遞減區(qū)間是.③當(dāng)時(shí),故的單調(diào)遞增區(qū)間是. ④當(dāng)時(shí),在區(qū)間和上,;在區(qū)間
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