Rolle's theorem

Suppose a continuous function (see continuity) crosses the x-axis at two points a and b and is differentiable at all points between a and b; that is it has a tangent at all points on the curve between a and b. Then there is at least one point between a and b where the derivative is 0, and the tangent is parallel to the x-axis.

Related category

• CALCULUS AND ANALYSIS

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