導(dǎo)數(shù)大題經(jīng)典(重點(diǎn)討論)練習(xí)及答案(整理、理科)-全文預(yù)覽
【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(méi)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(méi)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(méi)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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