设w>0,若函数f(x)=2sinwx在[-π/3,π/4]上单调递增,则w的取值范围是多少这里有解答,2kπ-π/2

Question

设w>0,若函数f(x)=2sinwx在[-π/3,π/4]上单调递增,则w的取值范围是多少
这里有解答,
2kπ-π/2

Answer 1

设w＞0,若函数f[x]=2sinwx在[-π\3,π\4]上单调递增,则w的取值范围是
解析：∵函数f[x]=2sinwx（w>0）在[-π\3,π\4]上单调递增
f(x)单调增区间：wx∈[2kπ-π/2,2kπ+π/2]==>x∈[2kπ/w-π/(2w),2kπ/w+π/(2w)]
区间[-π/3,π/4]包含于[2kπ/w-π/(2w),2kπ/w+π/(2w)]
∴-π/(2w)-1/(2w)w=π/4==>1/(2w)>=1/4==>w