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Rolle’s theorem - Derivative Applications

Rolle’s theorem

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Notes:

Let f(x)f(x) satisfy the three following conditions:

1) f(x)f(x) is continuous on the interval [a,b][a, b]

2) f(x)f(x) is differentiable on the interval (a,b)(a, b)

3) f(a)=f(b)f(a) = f(b)

If the conditions are fulfilled, then Rolle’s Theorem states that there must be a number (call it cc) such that a<c<ba < c < b and f(c)=0f'(c) = 0.

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    Rolle’s Theorem Overview
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Rolle’s theorem

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