The Cauchy mean-value theorem states that if f and g are two functions continuous on [a,b] and differentiable on (a,b), then there exists a point c in (a,b) such that f´(c)(g(b)-g(a)) = g´(c)(f(b)-f(a)) Geometric interpretation: Consider the parametric curve X(t) = (f(t), g(t)), t in [a,b], X(a)≠X(b); then the line passing through X(a), X(b) is parallel to the tangent line passing through X(c)Continuous functions, differentiable functions, parametric curves, mean-value theoremComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemática