Rolle's Theorem

Rolle’s Theorem

If a function f(x) defined on [a,b] is

continuous on [a,b]

differentiable in (a,b) and f(a) = f(b)

then there exists c∈(a,b) such that f'(c) = 0

Geometrical Interpretation of Rolle’s Theorem

Let f(x) be a function defined on [a,b] such that the curve y=f(x) is continuous between points (a,f(a)) and (b,f(b)); at every point on the curve, except at the points, it is possible to draw a unique tangent and ordinates at x=a and x=b [i.e. f(a) and f(b)] are equal. Then there exists at least one point on the curve where tangent is parallel to x-axis.