如图是y=f(x)=a/3*x³-2x²+3a²x的导函数y=f’(x)的简图,它与x轴的交点是(1,0)和(3,0)①求y=f(x)的极小值点和单调减区间②求实数a的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 03:32:43
![如图是y=f(x)=a/3*x³-2x²+3a²x的导函数y=f’(x)的简图,它与x轴的交点是(1,0)和(3,0)①求y=f(x)的极小值点和单调减区间②求实数a的值](/uploads/image/z/2682211-67-1.jpg?t=%E5%A6%82%E5%9B%BE%E6%98%AFy%3Df%28x%29%3Da%2F3%2Ax%26%23179%3B-2x%26%23178%3B%2B3a%26%23178%3Bx%E7%9A%84%E5%AF%BC%E5%87%BD%E6%95%B0y%3Df%E2%80%99%28x%29%E7%9A%84%E7%AE%80%E5%9B%BE%2C%E5%AE%83%E4%B8%8Ex%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9%E6%98%AF%EF%BC%881%2C0%EF%BC%89%E5%92%8C%EF%BC%883%2C0%EF%BC%89%E2%91%A0%E6%B1%82y%3Df%28x%29%E7%9A%84%E6%9E%81%E5%B0%8F%E5%80%BC%E7%82%B9%E5%92%8C%E5%8D%95%E8%B0%83%E5%87%8F%E5%8C%BA%E9%97%B4%E2%91%A1%E6%B1%82%E5%AE%9E%E6%95%B0a%E7%9A%84%E5%80%BC)
如图是y=f(x)=a/3*x³-2x²+3a²x的导函数y=f’(x)的简图,它与x轴的交点是(1,0)和(3,0)①求y=f(x)的极小值点和单调减区间②求实数a的值
如图是y=f(x)=a/3*x³-2x²+3a²x的导函数y=f’(x)的简图,它与x轴的交点是(1,0)和(3,0)
①求y=f(x)的极小值点和单调减区间
②求实数a的值
如图是y=f(x)=a/3*x³-2x²+3a²x的导函数y=f’(x)的简图,它与x轴的交点是(1,0)和(3,0)①求y=f(x)的极小值点和单调减区间②求实数a的值
①由图可得:y'=f'(x)=0时,x=1或3,
∴列出下表
x (-∞,1) 1 (1,3 ) 3 (3,+∞)
f'(x) + 0 - 0 +
f(x) ↑ 极大 ↓ 极小 ↑
∴f(x)的极小点为x=3,单调减区间是(1,3)
②∵y=f(x)=a/3*x³-2x²+3a²x
∴y'=f’(x)=ax²-4x+3a²,它过(1.0)和(3,0)
∴0=a-4+3a²且0=9a-12+3a²
解得a=1
求导最基础的题目啊····带进去算就可以了啊