Rolle's Theorem | Rolle Theorem

In calculus, Rolle's theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero.

Topics in calculus
Fundamental theorem Limits of functions Continuity Mean value theorem Rolle's theorem
Differential calculus Derivative Second derivative Third derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities Power rule Product rule Quotient rule Sum rule Chain rule
Integral calculus Lists of integrals Improper integral Multiple integral Integration by parts disks cylindrical shells substitution trigonometric substitution partial fractions changing order
Vector calculus Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem
Multivariable calculus Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian

Famous quotes containing the word theorem:

“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)