题目
若-π/2≤x≤π/2,求f(x)=√3sinx+cosx的最大值和最小值,并求出此时的x的值
提问时间：2021-04-27
答案
f(x)=2(√3/2sinx+1/2cosx)
=2(sinxcosπ/6+cosxsinπ/6)
=2sin(x+π/6)
-π/2<=x<=π/2
-π/3<=x+π/6<=2π/3
所以x+π/6=-π/3,sin(x+π/6)最小=-√3/2
x+π/6=π/2,sin(x+π/6)最大=1
所以
x=-π/2,f(x)最小=-√3
x=π/3,f(x)最大=2
=2(sinxcosπ/6+cosxsinπ/6)
=2sin(x+π/6)
-π/2<=x<=π/2
-π/3<=x+π/6<=2π/3
所以x+π/6=-π/3,sin(x+π/6)最小=-√3/2
x+π/6=π/2,sin(x+π/6)最大=1
所以
x=-π/2,f(x)最小=-√3
x=π/3,f(x)最大=2
举一反三
我想写一篇关于奥巴马的演讲的文章,写哪一篇好呢?为什么好
奥巴马演讲不用看稿子.为什么中国领导演讲要看?
想找英语初三上学期的首字母填空练习……
英语翻译
1,人们染上烟瘾,最终因吸烟使自己丧命.
最新试题
- 1关于运动的英语作文,60词左右.
- 2“Which letter does not belong in the following series?”的汉语解释.
- 3英语翻译
- 4开关短路是什么
- 5草木知春不久归 ,百般红紫斗芳菲 .杨花榆荚无才思 ,唯解漫天作雪飞
- 6The of childred in the small village is very difficult 八上英语6单元
- 7This is to certify that the Quality Management System of HUADI STEEL GROUP CO,LTD.怎么翻译
- 8一辆在高速公路上以108km/h行驶的汽车，它的速度为_m/s．
- 9All __ will be present at the conference.A parties concerned B parties concering
- 10在脲醛树脂合成中,尿素和甲醛哪个对ph影响最大 为什么
热门考点