Determine if the requirements for Rolle's theorem are met by the function f(x) = 5x + +3 guaranteed by the theorem. O When evaluated, a.) Ax) is continuous and differentiable on any interval not including 0; therefore, it is continuous on d.) The values guaranteed by Rolle's theorem are C--1 and c-1. where x-0, so fix) is differentiable on Theorem are not met. (3) = = 26 and f(5)-26. Therefore, f(a)-f(b) and the conditions of Rolle's theorem are met. (1₁5)₁ b.) fix) is continuous on any interval not including O; therefore, it is continuous on [₁5] Also, f(x) is differentiable everywhere except ·√(7)= |=2 and f(5)-26. Therefore, f(a) f(b) and the conditions of Rolle's fix) is continuous on on the interval - [ 3.5] = When evaluated, c.) [135] fix) is continuous on any interval not including O; therefore, it is continuous on the conditions of Rolle's theorem have not been met. 5 on [3.5] and If so, find the values of cin The value guaranteed by Rolle's theorem is c-1. and differentiable on (3)= = 26 and f(5)-26, Therefore, f(a)-f(b) and the conditions of Rolle's theorem are met. and fix) is differentiable everywhere except where x-0, so fix) is differentiable on Also, fix) is not differentiable on n (7.5).. Therefore, When evaluated,