设函数f(x)=【(x+2)²+sinx】/(x²+4)的最大值为M,最小值为m,则M+m=?
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![设函数f(x)=【(x+2)²+sinx】/(x²+4)的最大值为M,最小值为m,则M+m=?](/uploads/image/z/2624882-50-2.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%E3%80%90%EF%BC%88x%2B2%EF%BC%89%26%23178%3B%2Bsinx%E3%80%91%2F%EF%BC%88x%26%23178%3B%2B4%EF%BC%89%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BAM%2C%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BAm%2C%E5%88%99M%2Bm%3D%3F)
设函数f(x)=【(x+2)²+sinx】/(x²+4)的最大值为M,最小值为m,则M+m=?
设函数f(x)=【(x+2)²+sinx】/(x²+4)的最大值为M,最小值为m,则M+m=?
设函数f(x)=【(x+2)²+sinx】/(x²+4)的最大值为M,最小值为m,则M+m=?
f(x)=【(x+2)²+sinx】/(x²+4)
= 【x² + 4x +4+sinx】/(x²+4)
= 1 + (4x +sinx)/(x²+4)
设x= t时取到最大值M=1 + (4t +sint)/(t²+4)
则x = -t 时取到最小值m =1 + (4(-t) +sin(-t))/((-t)²+4)= 1- (4t +sint)/(t²+4)
所以 M+m = 2