Question

已知f(x)=(m+1)x2+2mx+1,若f(x)在[1,+∞)上是增函数,则m的取值范围是

Answer 1

由f(x)在[1,正无穷]上是增函数可知：m+1>0,即m > -1 可知：f(x)的对称轴是：x = -m/(m+1),则有：-m/(m+1) ≤1,解得：m≥-1/2所以：m的范围为：m ≥ -1/2