已知函数f(x)=ln(x^2-ax+3)在区间(-无穷大,a/2]上单调递减,则实数a的取值范围是
问题描述:
已知函数f(x)=ln(x^2-ax+3)在区间(-无穷大,a/2]上单调递减,则实数a的取值范围是
答
f(x)=ln(x^2-ax+3)令g(x)=x^2-ax+3则,f(x)在(-无穷大,a/2]上单调递减意味着g(x)在此区间为单调递减x^2-ax+3=(x-a/2)^2+3-a^2/4其对称轴为x=a/2,在(-无穷,a/2]上就是减函数但还要保证g(x)的值域为恒大于0所以就是3-...