Consider the initial value problem (at time to = 1): " = f(x) = (x - a)1/", ack, n>lodd, x(1) = To (A) Find the largest set A C R where f is continuous, and the largest set B C R where f is continuously differentiable. (B) Using the Existence and Uniqueness Theorem from class, find all possible initial values In at to = 1 for which the above initial value problem has a unique solution in some time interval around to = 1. (C) For the remaining initial values ro at to = 1, find at least 4 different solutions. (D) Finally, consider the special case a = 1, n = 3 and ro = 0, namely the following initial value problem: Ji = (x - 1)1/3, I(1) =0 Using (C), explain why there is a unique solution to this problem in some time interval around to = 1. Find that solution explicitly and find the largest time interval / E R in which this solution makes sense. This solution can be extended to all of R: find an extension and explain why this extension is not unique. (Hint: recall (A).)