题目

若函数f（x）=在x=x0处取得极值，则x0=　　　　　　．                    答案：3　．                                                                                                  【分析】求得函数f（x）的导数，由导数大于0，可得增区间；导数小于0，可得减区间．进而得到函数的极大值点，即可得到所求值．                                                                                      【解答】解：函数f（x）=的导数为f′（x）==，                     由x＞3时，f′（x）＜0，可得f（x）在（3，+∞）递减；                                由x＜3时，f′（x）＞0，可得f（x）在（﹣∞，3）递增．                               即有f（x）在x=3处取得极大值．                                                           由题意可得x0=3．                                                                              故答案为：3．                                                                                    【点评】本题考查导数的运用：求单调区间和极值，考查运算能力，属于基础题．                     　                                                                                                      

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