7．设函数在.处取得极值.且． (Ⅰ)若.求的值.并求的单调区间, (Ⅱ)若.求的取值范围．解:．①············································——青夏教育精英家教网—

7．设函数在.处取得极值.且． (Ⅰ)若.求的值.并求的单调区间, (Ⅱ)若.求的取值范围．解:．①················································································ 2分 (Ⅰ)当时. , 由题意知为方程的两根.所以．由.得．··························································································· 4分从而.．当时.,当时.．故在单调递减.在.单调递增．···································· 6分 (Ⅱ)由①式及题意知为方程的两根. 所以．从而. 由上式及题设知．························································································· 8分考虑. ．········································································ 10分故在单调递增.在单调递减.从而在的极大值为．又在上只有一个极值.所以为在上的最大值.且最小值为．所以.即的取值范围为．··············································· 14分【查看更多】

题目列表(包括答案和解析)

（辽宁卷文22）设函数在，处取得极值，且．