Rolle's Theorem

This Video explains how and when Rolle's Theorem can be applied. Rolle's Theorem requires that the function meet certain conditions across an interval. OPEN and CLOSED intervals It defines open and closed intervals The three conditions to be satisfied are:- CONTINUOUS across a CLOSED Interval It explains how to determine whether the function is continuous across a closed interval. DIFFERENTIABLE across an OPEN Interval. It explains how to determine whether the function is differentiable across an open interval. The ENDPOINT Y Values must be equal F(a) = F(b) It explains how to evaluate the Y values of the endpoints If all conditions are satisfied it demonstrates how to apply Rolle's Theorem by finding the derivative and setting it to zero, thus finding a point on the x axis where the tangent to the curve is parallel to the x-axis or where the derivative of f(x) =0 The video uses two worked example on the use of Rolle's Theorem. X: @johnsmathsbook Linked In: https://linkedin.com/in/john-ellis-0163ba322