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Rolle's Theorem
If $$f(x)$$ is continuous on $$[a,b]$$, differentiable on $$(a,b)$$, and:
$$f(a)=f(b)$$
then there exists at least one $$c\in(a,b)$$ such that:
$$f'(c)=0$$
Usage
- Used to prove the existence of a point where the derivative is zero.
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Rolle's Theorem
If $$f(x)$$ is continuous on $$[a,b]$$, differentiable on $$(a,b)$$, and:
$$f(a)=f(b)$$
then there exists at least one $$c\in(a,b)$$ such that:
$$f'(c)=0$$
Usage
- Used to prove the existence of a point where the derivative is zero.
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