Prove the Generalized Rolle's Theorem, Theorem 1.10, by verifying the following. a. Use

Chapter 1, Problem 26

(choose chapter or problem)

Prove the Generalized Rolle's Theorem, Theorem 1.10, by verifying the following. a. Use Rolle's Theorem to show that / (z,) = 0 for n 1 numbers in [a, b] with a < z\ < Zi < < Zn-i < b. b. Use Rolle's Theorem to show that / (vv,) 0 for n 2 numbers in [a, h] with 21 < wq < zi < W2 VVn_2 < Zn-I < b. c. Continue the arguments in parts (a) and (b) to show that for each j 1,2,... , n 1, there are n j distinct numbers in [a, b], where / (,) is 0. d. Show that part (c) implies the conclusion ofthe theorem