摘要：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

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