已知函数f(x)=sin^2x+sinxcosx (1)当0≤x≤派/2 求其最值及相应的x值已知函数f(x)=sin^2x+sinxcosx(1)当0≤x≤派/2 求其最值及相应的x值(2)试求不等式f(x)≥1的解集
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![已知函数f(x)=sin^2x+sinxcosx (1)当0≤x≤派/2 求其最值及相应的x值已知函数f(x)=sin^2x+sinxcosx(1)当0≤x≤派/2 求其最值及相应的x值(2)试求不等式f(x)≥1的解集](/uploads/image/z/14595247-55-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dsin%5E2x%2Bsinxcosx+%EF%BC%881%EF%BC%89%E5%BD%930%E2%89%A4x%E2%89%A4%E6%B4%BE%2F2+%E6%B1%82%E5%85%B6%E6%9C%80%E5%80%BC%E5%8F%8A%E7%9B%B8%E5%BA%94%E7%9A%84x%E5%80%BC%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dsin%5E2x%2Bsinxcosx%EF%BC%881%EF%BC%89%E5%BD%930%E2%89%A4x%E2%89%A4%E6%B4%BE%2F2+++%E6%B1%82%E5%85%B6%E6%9C%80%E5%80%BC%E5%8F%8A%E7%9B%B8%E5%BA%94%E7%9A%84x%E5%80%BC%EF%BC%882%EF%BC%89%E8%AF%95%E6%B1%82%E4%B8%8D%E7%AD%89%E5%BC%8Ff%EF%BC%88x%EF%BC%89%E2%89%A51%E7%9A%84%E8%A7%A3%E9%9B%86)
已知函数f(x)=sin^2x+sinxcosx (1)当0≤x≤派/2 求其最值及相应的x值已知函数f(x)=sin^2x+sinxcosx(1)当0≤x≤派/2 求其最值及相应的x值(2)试求不等式f(x)≥1的解集
已知函数f(x)=sin^2x+sinxcosx (1)当0≤x≤派/2 求其最值及相应的x值
已知函数f(x)=sin^2x+sinxcosx
(1)当0≤x≤派/2 求其最值及相应的x值
(2)试求不等式f(x)≥1的解集
已知函数f(x)=sin^2x+sinxcosx (1)当0≤x≤派/2 求其最值及相应的x值已知函数f(x)=sin^2x+sinxcosx(1)当0≤x≤派/2 求其最值及相应的x值(2)试求不等式f(x)≥1的解集
1f(x)=(sinx)^2+sinxcosx
=(1-cos(2x))/2+sin(2x)/2
=sin(2x)/2-cos(2x)/2+1/2
=(√2/2)*sin(2x-π/4)+1/2
因为
0≤x≤π/2
-π/4≤2x-π/4≤3π/4
所以-√2/2≤sin(2x-π/4)≤1
那么0≤f(x)≤(1+√2)/2
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1f(x)=(sinx)^2+sinxcosx
=(1-cos(2x))/2+sin(2x)/2
=sin(2x)/2-cos(2x)/2+1/2
=(√2/2)*sin(2x-π/4)+1/2
因为
0≤x≤π/2
-π/4≤2x-π/4≤3π/4
所以-√2/2≤sin(2x-π/4)≤1
那么0≤f(x)≤(1+√2)/2
即最大值是(1+√2)/2,最小值是0
2. f (x)≥1
(√2/2)*sin(2x-π/4)+1/2≥1
sin(2x-π/4) =(√2/2)
(2x-π/4)=π/4
2X=π/2
x=π/4
收起
(1)
f(x) = (sinx)^2 + sinxcosx
= (1/2)(1-cos2x) + (1/2)sin2x
= (1/2) + (√2/2)sin(2x-π/4)
0≤x≤π/2
0≤f(x)≤ (1/2)(1+√2)
(2)
f(x)≥1
(1/2) + (√2/2)sin(2x-π/4)≥1
sin(2x-π/4)≥ 1/√2
2kπ+ π/4≤2x-π/4 ≤ (2k+1)π- π/4
kπ+π/4≤ x ≤ (2k+1)π/2