The last sentence of part (D) of Kritik 2 has been simplified: I only ask for the extension of the solution, and nothing about uniqueness. Please take a look at the new version of the assignment on Kritik. I have given an extension for Kritik 2 until tomorrow 11pm (Thursday Oct 7th, 11pm)
When grading part (D), only grade up to and including the extension of the solution, i.e. do not grade the last part about the unique extension.
BTW, this last part of (D) is a very good question: you should decide whether the extention in this problem is unique or not, and what does this means in terms of the condition that f be C^1 for uniqueness.