作业帮函数f(x)=ax²+1(a>0),g(x)=x³+bx,当a=3,b=-9时,若函数f(x）+g(x)在区间[k,2]上的最大值为28,求k的取值范围
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![函数f(x)=ax²+1(a>0),g(x)=x³+bx,当a=3,b=-9时,若函数f(x）+g(x)在区间[k,2]上的最大值为28,求k的取值范围](/uploads/image/z/468756-36-6.jpg?t=%E5%87%BD%E6%95%B0f%28x%29%3Dax%26%23178%3B%2B1%28a%3E0%29%2Cg%28x%29%3Dx%26%23179%3B%2Bbx%2C%E5%BD%93a%3D3%2Cb%3D-9%E6%97%B6%2C%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%EF%BC%89%2Bg%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5Bk%2C2%5D%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E4%B8%BA28%2C%E6%B1%82k%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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函数f(x)=ax²+1(a>0),g(x)=x³+bx,当a=3,b=-9时,若函数f(x）+g(x)在区间[k,2]上的最大值为28,求k的取值范围
函数f(x)=ax²+1(a>0),g(x)=x³+bx,
当a=3,b=-9时,若函数f(x）+g(x)在区间[k,2]上的最大值为28,求k的取值范围
函数f(x)=ax²+1(a>0),g(x)=x³+bx,当a=3,b=-9时,若函数f(x）+g(x)在区间[k,2]上的最大值为28,求k的取值范围
令h(x)=f(x)+g(x)=3x^2+1+x^3-9x
h'(x)=6x+3x^2-9=3(x^2+2x-3)=3(x+3)(x-1)=0,得极值点x=-3,1
x>1或x