作业帮f（x）=2X-X² =-(x²-2x+1)+1 =-(x-1)²+1 函数f（x）=2X-X²的增区间:(-∞,1]为什么算出-(x-1)²+1后就得出 :(-∞,1]
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 02:46:31
![f（x）=2X-X² =-(x²-2x+1)+1 =-(x-1)²+1 函数f（x）=2X-X²的增区间:(-∞,1]为什么算出-(x-1)²+1后就得出 :(-∞,1]](/uploads/image/z/2737152-0-2.jpg?t=f%EF%BC%88x%EF%BC%89%3D2X-X%26%23178%3B+%3D-%28x%26%23178%3B-2x%2B1%29%2B1+%3D-%28x-1%29%26%23178%3B%2B1+%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D2X-X%26%23178%3B%E7%9A%84%E5%A2%9E%E5%8C%BA%E9%97%B4%3A%28-%E2%88%9E%2C1%5D%E4%B8%BA%E4%BB%80%E4%B9%88%E7%AE%97%E5%87%BA-%28x-1%29%26%23178%3B%2B1%E5%90%8E%E5%B0%B1%E5%BE%97%E5%87%BA+%3A%28-%E2%88%9E%2C1%5D)
f（x）=2X-X² =-(x²-2x+1)+1 =-(x-1)²+1 函数f（x）=2X-X²的增区间:(-∞,1]为什么算出-(x-1)²+1后就得出 :(-∞,1]
f（x）=2X-X² =-(x²-2x+1)+1 =-(x-1)²+1 函数f（x）=2X-X²的增区间:(-∞,1]
为什么算出-(x-1)²+1后就得出 :(-∞,1]
f（x）=2X-X² =-(x²-2x+1)+1 =-(x-1)²+1 函数f（x）=2X-X²的增区间:(-∞,1]为什么算出-(x-1)²+1后就得出 :(-∞,1]
因为这是一个开口向下的抛物线,顶点（1,1）,所以在:(-∞,1]递增,在:[1,+∞)递减
由-(x-1)²+1可以得到它的对称轴为1，又因为a=-1＜0所以开口向下，由图像就可以判断该函数在:(-∞,1]上单调递增