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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?