for 4 a) as far as I know, f'(x) for x>0 is 2x, and that for x

theoretically speaking 4b) should be asking me to prove f'(x) exists on the premise that it does(it can be proved existing), however, in 4 a) it is calculated that the function can yield two possible answers: 2x and -2x, when being differentiated;

now, even we assume that if x is not confined to be smaller () than 0, that when x=0, the derivative of 0 still, is non-existential. Kindly ask if it is possible to be proved existing within the syllabus of Calculus I (as easy as possible), or by any chance, that my deduction is correct that it is non-existential, if so, how may I prove it non-existetial, thank you!

Let x): xix]. (a) Find x) for x > 0 and x