Question

已知函數(shù)f(x)=Asin(ωx+φ)+1(A＞0，ω＞0，0＜φ＜π)，其導(dǎo)函數(shù)f′(x)的部分圖像如圖所示，則y=f(x)的解析式是    (    )

A.f(x)=4sin(x+)+1                   B.f(x)=4sin(+)+1

C.f(x)=2sin(+)+1                 D.f(x)=4cos(+)+1

Answer 1

答案：B  【解析】本題考查函數(shù)的導(dǎo)數(shù)公式,余弦型函數(shù)的圖像及性質(zhì)等知識.對原函數(shù)根據(jù)復(fù)合函數(shù)求導(dǎo)法則求導(dǎo),得f′(x)=ωAcos(ωx+).觀察圖像得從到為函數(shù)的個周期,即,所以T==4π,因為ω＞0,∴ω=；又結(jié)合此函數(shù)的圖像,其函數(shù)的最大值為2,最小值為-2,得|ωA|=2.而A＞0,所以A=4.即導(dǎo)函數(shù)的解析式為f′(x)=4cos(x+).又點(,0)在其圖像上,代入得cos(+)=0,0＜＜π,∴=.于是得原函數(shù)的解析式f(x)=4sin()+1.