已知函数f(x)=ax^3+bx^2+cx在点x0处取得的极大值是5,其导函数y=f(x)的图像经过(1,0)(2,0)求(1)x0=?(2)求a,b,c的值?RT,要让我看的懂哦,
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![已知函数f(x)=ax^3+bx^2+cx在点x0处取得的极大值是5,其导函数y=f(x)的图像经过(1,0)(2,0)求(1)x0=?(2)求a,b,c的值?RT,要让我看的懂哦,](/uploads/image/z/2094673-49-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dax%5E3%2Bbx%5E2%2Bcx%E5%9C%A8%E7%82%B9x0%E5%A4%84%E5%8F%96%E5%BE%97%E7%9A%84%E6%9E%81%E5%A4%A7%E5%80%BC%E6%98%AF5%2C%E5%85%B6%E5%AF%BC%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E5%9B%BE%E5%83%8F%E7%BB%8F%E8%BF%87%EF%BC%881%2C0%EF%BC%89%EF%BC%882%2C0%EF%BC%89%E6%B1%82%281%29x0%3D%3F%282%29%E6%B1%82a%2Cb%2Cc%E7%9A%84%E5%80%BC%3FRT%2C%E8%A6%81%E8%AE%A9%E6%88%91%E7%9C%8B%E7%9A%84%E6%87%82%E5%93%A6%2C)
已知函数f(x)=ax^3+bx^2+cx在点x0处取得的极大值是5,其导函数y=f(x)的图像经过(1,0)(2,0)求(1)x0=?(2)求a,b,c的值?RT,要让我看的懂哦,
已知函数f(x)=ax^3+bx^2+cx在点x0处取得的极大值是5,其导函数y=f(x)的图像经过(1,0)(2,0)
求
(1)x0=?
(2)求a,b,c的值?
RT,要让我看的懂哦,
已知函数f(x)=ax^3+bx^2+cx在点x0处取得的极大值是5,其导函数y=f(x)的图像经过(1,0)(2,0)求(1)x0=?(2)求a,b,c的值?RT,要让我看的懂哦,
f(x) = ax^3 + bx^2 + cx
f'(x) = 3ax^2 + 2bx + c,
0 = f'(1) = 3a + 2b + c,...(1)
0 = f'(2) = 12a + 4b + c....(2)
因方程有2个不同的根,所以 a 不等于0.
0 = 9a + 2b,
2b = -9a.
f''(x) = 6ax + 2b
f''(1) = 6a + 2b = 6a - 9a = -3a,
f''(2) = 12a + 2b = 12a - 9a = 3a.
若a < 0.
则 f''(2) < 0.f'(2) = 0.f(x) 在 x = 2处达到极大值5.
5 = f(2) = 8a + 4b + 2c....(3)
由(1),(2),(3)解得
a = 5/2与a < 0矛盾.
所以,
a > 0.
则 f''(1) < 0.f'(1) = 0.f(x) 在 x = 1处达到极大值5.
5 = f(1) = a + b + c....(4)
由(1),(2),(4)解得
a = 2,b = -9,c = 12.
因此,
x0 = 1.