已知曲线y=ax3+bx2+cx+d满足下列条件:①过原点;②在x=0处导数为-1;③在x=1处切线方程为y=4x-3.(Ⅰ) 求实数a、b、c、d的值;(Ⅱ)求函数y=ax3+bx2+cx+d的极值.解(Ⅰ)y′=3ax2+2bx+c根据条件
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![已知曲线y=ax3+bx2+cx+d满足下列条件:①过原点;②在x=0处导数为-1;③在x=1处切线方程为y=4x-3.(Ⅰ) 求实数a、b、c、d的值;(Ⅱ)求函数y=ax3+bx2+cx+d的极值.解(Ⅰ)y′=3ax2+2bx+c根据条件](/uploads/image/z/8936030-38-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%9B%B2%E7%BA%BFy%3Dax3%2Bbx2%2Bcx%2Bd%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%9D%A1%E4%BB%B6%EF%BC%9A%E2%91%A0%E8%BF%87%E5%8E%9F%E7%82%B9%EF%BC%9B%E2%91%A1%E5%9C%A8x%3D0%E5%A4%84%E5%AF%BC%E6%95%B0%E4%B8%BA-1%EF%BC%9B%E2%91%A2%E5%9C%A8x%3D1%E5%A4%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%E4%B8%BAy%3D4x-3%EF%BC%8E%EF%BC%88%E2%85%A0%EF%BC%89+%E6%B1%82%E5%AE%9E%E6%95%B0a%E3%80%81b%E3%80%81c%E3%80%81d%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%88%E2%85%A1%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0y%3Dax3%2Bbx2%2Bcx%2Bd%E7%9A%84%E6%9E%81%E5%80%BC%EF%BC%8E%E8%A7%A3%EF%BC%88%E2%85%A0%EF%BC%89y%E2%80%B2%3D3ax2%2B2bx%2Bc%E6%A0%B9%E6%8D%AE%E6%9D%A1%E4%BB%B6)
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