# How to use rolles theorem for #f(x)= (x^3/3)- 3x# on the interval [-3,3]?

For the function

we see that

This can be easily seen from the graph

graph{x^3/3-3 x [-5, 5, -5, 5]}

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To use Rolle's Theorem for ( f(x) = \frac{x^3}{3} - 3x ) on the interval ([-3, 3]), you need to check three conditions:

- Verify that the function ( f(x) ) is continuous on the closed interval ([-3, 3]).
- Confirm that ( f(x) ) is differentiable on the open interval ((-3, 3)).
- Ensure that ( f(-3) = f(3) ).

If all three conditions are met, then according to Rolle's Theorem, there exists at least one value ( c ) in the open interval ((-3, 3)) such that ( f'(c) = 0 ).

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