1.函数f（x）=2sin（πx+1/4）的最小正周期是?2.等差数列{an}中,a3＋3a8＋a13=120,则2a9－a10的值为?3.若函数f(x)=mx^2+x+5在[-2,正无穷]上是增函数,则m的取值范围是?

Question

1.函数f（x）=2sin（πx+1/4）的最小正周期是?
2.等差数列{an}中,a3＋3a8＋a13=120,则2a9－a10的值为?
3.若函数f(x)=mx^2+x+5在[-2,正无穷]上是增函数,则m的取值范围是?

Answer 1

1.最小正周期是2π/π = 2 (πx从0到2π,相当于x从0到2)
2.a3＋3a8＋a13=120
(a8 - 5d) + 3a8＋(a8 + 5d) = 5a8 = 120
a8 = 24
2a9 - a10 = 2(a8 + d) - (a8 +2d) = a8 = 24
3.函数f(x)=mx^2+x+5在[-2,正无穷]上是增函数,顶点的横坐标小于 -2 且抛物线开口向上,m> 0
-2 > -1/(2m)
m < 1/4
即 0 < m < 1/4