函数y=﹣3sin²x+12sinx-1(x∈R)的最大值是 A.11 B.8 C.-16 D.-1
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![函数y=﹣3sin²x+12sinx-1(x∈R)的最大值是 A.11 B.8 C.-16 D.-1](/uploads/image/z/11498271-15-1.jpg?t=%E5%87%BD%E6%95%B0y%3D%EF%B9%A33sin%26%23178%3Bx%2B12sinx-1%28x%E2%88%88R%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF+A.11+B.8+C.-16+D.-1)
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函数y=﹣3sin²x+12sinx-1(x∈R)的最大值是 A.11 B.8 C.-16 D.-1
函数y=﹣3sin²x+12sinx-1(x∈R)的最大值是
A.11 B.8 C.-16 D.-1
函数y=﹣3sin²x+12sinx-1(x∈R)的最大值是 A.11 B.8 C.-16 D.-1
y=﹣3sin²x+12sinx-1=y=﹣3(sinx-2)²+11,对x∈R,sin x∈[-1,1],y随sin x增大而增大,所以最大值为y=-3(1-2)²+11=8
y=-3((sinx)^2-4(sinx)+4)+12-1
=-3((sinx)-2)^2+11
因为-1<=sinx<=1
所以-3
y的值域是[-16,8]