f(x)=2sin^2x+cos^2x+sinxcosx,x∈R,f(π/12)f(x)=2sin^2x+cos^2x+sinxcosx,x∈R求:1) f(π/12)的值2) f(x)的最小值及相应x的值3) f(x)的递增区间

来源：学生作业帮助网 编辑：作业帮 时间：2024/08/07 10:20:01
f(x)=2sin^2x+cos^2x+sinxcosx,x∈R,f(π/12)f(x)=2sin^2x+cos^2x+sinxcosx,x∈R求:1) f(π/12)的值2) f(x)的最小值及相应x的值3) f(x)的递增区间
xSn@~=.z<WJT UPi Z!JPZ8" 4}CuS_Y։D-Gr|7V]J2{(i)0y~_:Zظ F$:Ş6[2[ݎS~k?Fw<\ k 1.E3f4֪!-Kٌg 藲yBIX+,`Rr%c*({aJrak=vLažyP<d,DX"OB8~0FRL/E+;>S`}}oCG S+I¬`jrzݼ:.vM}oi#ҡe$) y7Ïp msYo /ƴǮF&E8] G;aH<Ϯ4p'`?3vs}'!D|| ]|lN*]FQea`)rOd?S|&tp3ǣ Fđ

f(x)=2sin^2x+cos^2x+sinxcosx,x∈R,f(π/12)f(x)=2sin^2x+cos^2x+sinxcosx,x∈R求:1) f(π/12)的值2) f(x)的最小值及相应x的值3) f(x)的递增区间
f(x)=2sin^2x+cos^2x+sinxcosx,x∈R,f(π/12)
f(x)=2sin^2x+cos^2x+sinxcosx,x∈R
求:
1) f(π/12)的值
2) f(x)的最小值及相应x的值
3) f(x)的递增区间

f(x)=2sin^2x+cos^2x+sinxcosx,x∈R,f(π/12)f(x)=2sin^2x+cos^2x+sinxcosx,x∈R求:1) f(π/12)的值2) f(x)的最小值及相应x的值3) f(x)的递增区间
f(x) = 2sin^2x+cos^2x+sinxcosx
= 1 + sin^2x + 1/2sin2x
= 1 + (1 - cos2x)/2 + 1/2sin2x
= 3/2 + 1/2(sin2x - cos2x)
= 3/2 + 1/sqrt(2) (sin(2x - π/4))
所以f(π/12) = 3/2 + 1/sqrt(2) * sin(-π/12) = (7 - sqrt(3))/4
min(f(x)) = 3/2 - 1/sqrt(2) = (3 - sqrt(2))/2 此时 2x - π/4 = -π/2, x = -π/8
f(x)在[ -π/8 + kπ, 3π/8 + kπ]上递增

把函数化成单名函数：
f(x)=3/2+√2/2sin(2x+π/4)
下面应该很好做了。

f(x) = 2sin²x+cos²x+sinxcosx = sin²x+1+sin2x/2 = 3/2+(sin2x-cos2x)/2
1、f(π/12)=(7-√3)/4
2、f‘(x)=cos2x+sin2x=√2(sin(2x+π/4))=0解得x=kπ/2-π/4，对应最小值x=kπ-π/4，f(x)=1
3、f'(x)>=0时x在[kπ-π/4,3kπ/2-π/4],递增

f(x)=cos(2x)+2sin(x)化简 f'(sin^2x)=cos^2x,求f(x)f'((sin^x)^2)=(cos^x)^2 f(x)为奇函数,x>0,f(x)=sin 2x+cos x,则x 已知f(x)=cos(x/2)[sin(x/2)-cos(x/2)],其导为? f(x)=cos(2兀-x)cos(2/兀-x)-sin方x化简速求 f(sin x)=3-cos 2x,求f(cos x)=? 设f(sin x)=3-cos 2x,则f(cos x）=? 若F(sin x)=3-cos 2x 则F（cos x）=? 化简：f(x)=sin(x)cos(x)/sin(2x) f(sin x)=cos 2x +1 求 f(cos x) f(sin x)=3-cos 2x求f(cos x) f(cos x)=2-sin 2x,则f(sin x)=? 设f(sin x/2 )-1+cos x ,求f(x)、f(cos x/2 ). 设函数f(x)=p·q,其中向量p=(sin x,cos x+sin x),q=(2cos x,cos sin x) ( f(x)=(6sin^4x-7sin^2x+2)/(sin^2x-cos^2x) f(x)=cos(2x+60)+sin^2x 求f(x)的值域 f(x)=sin(x+π/4)图像怎样变成F(x)=cos(2x) 已知tan=2,求(cos x+sin x)/(cos x-sin x)+sin^2x