已知函数f(x)=1/3x^3+1/2ax^2+bx在区间[-1,1),(1,3]内各有一个极值点.(1)求a^2-4b的最大值.(2)当a^2-4b=8时,设函数y=f(x)在点A(1,f(1))处的切线为l,若l在点A处穿过函数y=f(x)的图像(即动点在点A附近沿
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![已知函数f(x)=1/3x^3+1/2ax^2+bx在区间[-1,1),(1,3]内各有一个极值点.(1)求a^2-4b的最大值.(2)当a^2-4b=8时,设函数y=f(x)在点A(1,f(1))处的切线为l,若l在点A处穿过函数y=f(x)的图像(即动点在点A附近沿](/uploads/image/z/3017168-8-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D1%2F3x%5E3%2B1%2F2ax%5E2%2Bbx%E5%9C%A8%E5%8C%BA%E9%97%B4%5B-1%2C1%EF%BC%89%2C%EF%BC%881%2C3%5D%E5%86%85%E5%90%84%E6%9C%89%E4%B8%80%E4%B8%AA%E6%9E%81%E5%80%BC%E7%82%B9.%EF%BC%881%EF%BC%89%E6%B1%82a%5E2-4b%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC.%EF%BC%882%EF%BC%89%E5%BD%93a%5E2-4b%3D8%E6%97%B6%2C%E8%AE%BE%E5%87%BD%E6%95%B0y%3Df%28x%29%E5%9C%A8%E7%82%B9A%281%2Cf%281%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E4%B8%BAl%2C%E8%8B%A5l%E5%9C%A8%E7%82%B9A%E5%A4%84%E7%A9%BF%E8%BF%87%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%28%E5%8D%B3%E5%8A%A8%E7%82%B9%E5%9C%A8%E7%82%B9A%E9%99%84%E8%BF%91%E6%B2%BF)
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