论文部分内容阅读
笔者在研读湖北省100所重点中学2011届高三联合考试数学文科卷第15题时,发现命题者提供的答案有待商榷.为便于说明,现给出题目并附参考答案:若对于任意t∈[1,2],函数g(x)=x~3+(m/2+2)x~2-2x在区间(t,3)上总不为单调函数,则实数m的取值范围是____.参考答案:g′(x)=3x~2+(m+4)x-2,若g(x)在区间(t,3)上总为单调函数,则①g′(x)
The author was studying the 15th question of the 100 mathematics subjects of the 2011 Senior Middle School Joint Examination of the 100 key middle schools in Hubei Province and found that the answers provided by the propositions were to be discussed. For the convenience of explanation, the title is given with reference to the answer: If for any t∈[ 1,2], the function g(x)=x~3+(m/2+2)x~2-2x is not a monotonous function in the interval (t,3). The range of the real number m is _ ___.Reference answer: g’(x)=3x~2+(m+4)x-2, if g(x) is always a monotonic function in the interval (t,3), then 1g’(x)