Existence and Uniqueness Theorem (Help)

Let , for .

(a)Show that satisfies a Lipschitz condition on with respect to . (Solved)

(b)Find the first 3 successive approximations , and of the initial value problem , . (Solved)

(c)State the largest interval in which a unique solution to the initial value problem in (b) is defined. (Solved)

(d)Let be the solution to the initial value problem in (b). Prove that , for all .

I've difficulty in doing the last questions. How do I go about doing the last question?

Thanks in advance.