首先考慮sinx,它是以2π為周期的函數(shù).
它的增區(qū)間是[2kπ-0.5π,2kπ+0.5π]
減區(qū)間是[2kπ+0.5π,2kπ+1.5π]
對于f(x)=Asin(ωx+φ)
A>0
(1)增區(qū)間
2kπ-0.5π≤ωx+φ≤2kπ+0.5π
(2kπ-0.5π-φ)/ω≤x≤(2kπ+0.5π-φ)/ω
(2)減區(qū)間
2kπ+0.5π≤ωx+φ≤2kπ+1.5π
(2kπ+0.5π-φ)/ω≤x≤(2kπ+1.5π-φ)/ω
這里k是任意整數(shù)
A0時(shí)正好相反.
(1)減區(qū)間
2kπ-0.5π≤ωx+φ≤2kπ+0.5π
(2kπ-0.5π-φ)/ω≤x≤(2kπ+0.5π-φ)/ω
(2)增區(qū)間
2kπ+0.5π≤ωx+φ≤2kπ+1.5π
(2kπ+0.5π-φ)/ω≤x≤(2kπ+1.5π-φ)/ω
A=0就一直是0了,無所謂增減.
感謝wangwei781999提醒.
另外修正了一個(gè)錯(cuò)字.