Question

In the second part of problem 1D-5, why do I need to go back and use the a + b = 1 of the first part? I'm still with the mindset that b can be any real number as it is not present in f'(x).

Answer 1

I made a mistake on this one the first time too: if f(x) isn't continuous, it isn't differentiable i.e. there will be no f'(x), therefore, for f'(x), not only that we need a=2, we also need a+b=1 so that f(x) is continuous.