作业帮设函数f(x)在[a,b]上连续,在（a,b）内可导,且f(a)=f(b),则曲线y=f(x)在（a,b）内平行于x轴的切线有几条?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 22:21:45
![设函数f(x)在[a,b]上连续,在（a,b）内可导,且f(a)=f(b),则曲线y=f(x)在（a,b）内平行于x轴的切线有几条?](/uploads/image/z/13201540-52-0.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%88a%2Cb%EF%BC%89%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%28a%29%3Df%28b%29%2C%E5%88%99%E6%9B%B2%E7%BA%BFy%3Df%28x%29%E5%9C%A8%EF%BC%88a%2Cb%EF%BC%89%E5%86%85%E5%B9%B3%E8%A1%8C%E4%BA%8Ex%E8%BD%B4%E7%9A%84%E5%88%87%E7%BA%BF%E6%9C%89%E5%87%A0%E6%9D%A1%3F)
设函数f(x)在[a,b]上连续,在（a,b）内可导,且f(a)=f(b),则曲线y=f(x)在（a,b）内平行于x轴的切线有几条?
设函数f(x)在[a,b]上连续,在（a,b）内可导,且f(a)=f(b),则曲线y=f(x)在（a,b）内平行于x轴的切线有几条?
设函数f(x)在[a,b]上连续,在（a,b）内可导,且f(a)=f(b),则曲线y=f(x)在（a,b）内平行于x轴的切线有几条?
求出f(x)在(a,b)上的极大值和极小值,如果极值不等于零,则那些极值所对应的平行于x轴的直线就是题目所求切线,如果极值为零,则这条为零的切线不符合题意（因为它就是x轴）.
由罗尔定理得在（a,b）间至少存在一个点导数为0，所以至少一条
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