设a属于R,函数f(x)=ax³-3x²,(1)若a=1,求f(x)的极值与单调区间,(2)若fx的图像在x=-1处的切线与直线y=3x平行,求a值,(3)若fx=ax³-3x²的图像与直线y=-2有三个公共点,求a的取值范围.
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![设a属于R,函数f(x)=ax³-3x²,(1)若a=1,求f(x)的极值与单调区间,(2)若fx的图像在x=-1处的切线与直线y=3x平行,求a值,(3)若fx=ax³-3x²的图像与直线y=-2有三个公共点,求a的取值范围.](/uploads/image/z/1790995-67-5.jpg?t=%E8%AE%BEa%E5%B1%9E%E4%BA%8ER%2C%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dax%26%23179%3B-3x%26%23178%3B%2C%EF%BC%881%EF%BC%89%E8%8B%A5a%3D1%2C%E6%B1%82f%28x%29%E7%9A%84%E6%9E%81%E5%80%BC%E4%B8%8E%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%2C%EF%BC%882%EF%BC%89%E8%8B%A5fx%E7%9A%84%E5%9B%BE%E5%83%8F%E5%9C%A8x%3D-1%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D3x%E5%B9%B3%E8%A1%8C%2C%E6%B1%82a%E5%80%BC%2C%EF%BC%883%EF%BC%89%E8%8B%A5fx%3Dax%26%23179%3B-3x%26%23178%3B%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8E%E7%9B%B4%E7%BA%BFy%3D-2%E6%9C%89%E4%B8%89%E4%B8%AA%E5%85%AC%E5%85%B1%E7%82%B9%2C%E6%B1%82a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
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设a属于R,函数f(x)=ax³-3x²,(1)若a=1,求f(x)的极值与单调区间,(2)若fx的图像在x=-1处的切线与直线y=3x平行,求a值,(3)若fx=ax³-3x²的图像与直线y=-2有三个公共点,求a的取值范围.
设a属于R,函数f(x)=ax³-3x²,(1)若a=1,求f(x)的极值与单调区间,(2)若fx的图像在x=-1处的切线与直线y=3x平行,求a值,(3)若fx=ax³-3x²的图像与直线y=-2有三个公共点,求a的取值范围.
设a属于R,函数f(x)=ax³-3x²,(1)若a=1,求f(x)的极值与单调区间,(2)若fx的图像在x=-1处的切线与直线y=3x平行,求a值,(3)若fx=ax³-3x²的图像与直线y=-2有三个公共点,求a的取值范围.
函数f(x)=ax³-3x²求导:
f(x)‘=3ax²-6x=3x(ax-2)