已知函数f（x）的定义域为（-2，2），其导函数f′（x）=x2+2cosx且f（0）=0，则关于实数x的不等式f（x-2）+f（x2-2x）＞0的解集为（ ）
|
f'（x）=x2+2cosx
知f（x）=
x3+2sinx+c而f（0）=0，1 3
∴c=0
即：f（x）=
x3+2sinx1 3
易知，此函数是奇函数，且在整个区间单调递增，
因为f'（x）=x2+2cosx在x∈（0，2）恒大于0
根据奇函数的性质可得出，在其对应区间上亦是单调递增的f（x-2）+f（x2-2x）＞0
f（x-2）＞-f（x2-2x）
即：f（x-2）＞f（2x-x2）
∴-2＜x-2＜2 -2＜2x-x2＜2 x-2＞2x-x2
解得：x∈（2，1+
）3
故选D．
| Teachers need to be aware of the emotional, intellectual, and physical changes that young adults experience. And they also need to give serious (21) to how they can be best (22) such changes. Growing bodies need movement and (23) , but not just in ways that emphasize competition. (24) they are adjusting to their new bodies and a whole host of new intellectual and emotional challenges, teenagers are especially self-conscious and need the (25) that comes from achieving success and knowing that their accomplishments are (26) by others. However, the typical teenage lifestyle is already filled with so much com petition that it would be (27) to plan activities in which there are more winners than losers, (28) , publishing newsletters with many student-written book reviews, (29) student artwork, and sponsoring book discussion clubs. A variety of small clubs can pro- vide (30) opportunities for leadership, as well as for practice in successful (31) dynamics. Making friends is extremely important to teenagers, and many shy students need the (32) of some kind of organization with a supportive adult (33) visible in the back-ground. In these activities, it is important to remember that the young teens have (34) attention spans. A variety of activities should be organized (35) participants can remain active as long as they want and then go on to something else without feeling guilty and with- out letting the other participants down. |
A．care
B．nutrition
C．exercise
D．leisure