The f(x) continuous display curves on 1 and [a, b] are seamless, including the endpoints;

2. The deduction that (a, b) contains f(x) shows that the curve y=f(x) has a tangent at every point;

3.f(a)=f(b) indicates that the secant (straight line AB) of the curve is parallel to the X axis; The direct geometric significance of the conclusion of Rolle's theorem is that at least one point ξ can be found in (a, b), so that f'(ξ)=0, which means that the tangent slope of at least one point on the curve is 0, so that the tangent is parallel to the secant AB and parallel to the X axis.

Extended data:

Rolle's mean value theorem is an important theorem in differential calculus and one of the three theorems of differential mean value. It is named after the French mathematician Raul. Rolle's theorem assumes that the function f(x) is continuous in the closed interval [a, b] (where a is not equal to b) and derivable in the open interval (a, b), and f(a)=f(b), then at least a little ξ∈(a, b) makes f' (ξ).

Raul has done a lot of work in algebra, and once actively used concise mathematical symbols such as "=" and "√ ~" to write mathematical works. Learn and master the concept of order of real number set and the elimination method of equation; A so-called cascade rule is proposed to separate the roots of algebraic equations.

People's Network —— Summary of Important Knowledge Points of Mathematics for Postgraduate Entrance Examination in 2065438+05