Euclid's Muse

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By Irina Lyublinskaya
Exploring Rolle's Theorem
Explore conditions of the Rolle's Theorem. The applet shows the graph of continuous differentiable function f(x) on a closed interval  [a, b]. Case 1.  f(x) < f(a) for some x inside the interval (a, b). Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0? Case 2.  f(x) > f(a) for some x inside the interval (a, b). Can you find the number  c such that f'(c)=0? What did you notice about the point when f'(c)=0? Can a given function have more than one number on a given interval such that f'(c)=0?

Tags: Calclulus

By Phil Todd
Moving point
We watch a point move according to a given displacement graph (which we can edit)

Tags: function, motion, displacement


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