15.下面四个图象中,有一个是函数f(x)=$\frac{1}{3}$x3+ax2+(a2-1)x+1(a∈R)的导函数y=f′(x)的图象,则f(-1)=( )
A. | $\frac{5}{3}$或$-\frac{1}{3}$ | B. | $\frac{5}{3}$或$\frac{1}{3}$ | C. | $-\frac{1}{3}$或$-\frac{5}{3}$ | D. | $\frac{1}{3}$或$-\frac{5}{3}$ |
14.已知m∈R,函数f(x)=$\left\{\begin{array}{l}{|x+1|,}&{x<1}\\{lg(x-1),}&{x>1}\end{array}\right.$,g(x)=x2-2x+2m-2,若函数y=f(g(x))-m有6个零点,则实数m的取值范围是( )
A. | (1,2) | B. | ($\frac{3}{4}$,1) | C. | ($\frac{2}{3}$,$\frac{3}{4}$) | D. | (0,$\frac{2}{3}$) |
13.在△ABC中,角A、B、C的对边分别是a、b、c,其中b=c=2,若函数f(x)=$\frac{1}{4}{x^3}-\frac{3}{4}x$的极大值是cosA,则△ABC的面积等于( )
A. | 1 | B. | $\sqrt{3}$ | C. | 2 | D. | 2$\sqrt{3}$ |
12.若函数$f(x)=-\frac{1}{2}{({x-2})^2}+alnx$在(1,+∞)上是减函数,则实数a的取值范围是( )
0 251716 251724 251730 251734 251740 251742 251746 251752 251754 251760 251766 251770 251772 251776 251782 251784 251790 251794 251796 251800 251802 251806 251808 251810 251811 251812 251814 251815 251816 251818 251820 251824 251826 251830 251832 251836 251842 251844 251850 251854 251856 251860 251866 251872 251874 251880 251884 251886 251892 251896 251902 251910 266669
A. | .[-1,+∞) | B. | (-∞,-1] | C. | (1,+∞) | D. | .(-∞,1] |