Please make sure that your work is clearly legible and includes every steps, and then upload your written solution as a pdf or word file.

1) Use the Chain Rule to express the second derivative of f o g in terms of the rst and second derivatives of j and g. 1 1 a: 2) Show that a: = and 2 are inverses. ) 1 + m gm 3 y'( ) 9' (m) 1 Then compute :1: directly. And verify that = . f' (960)) 3) Show that for any constants M, k. and a, the function y 0) for all :1: E (a, b). Prove that there eXlStS c E (31b) such that u) = E -l- E' (Hlnt. consider I I the function is: \"I: : 0. If there exists a funcon 9(3) such thatg' (m) = if: _ _ hen g' (C) = Oyields 55) = + i Now nd such 9 (3:) and use MVT to show the existence of such c E (a, (1).)