Examples of Darboux's Theorem
Instructions
The dynamic activity below shows two examples of Darboux's Theorem. Select different pages to check the two examples. You can change the given intervals [a, b]. Slide f(c) and observe the corresponding f'(c).
Reflection Questions
For all the values M between f'(a) and f'(b), can you find a point c in (a, b) such that f'(c)=M? What are the relations between the tangent lines at x=a, x=b, and x=c?