In this question you will need to read and understand the following definition, proposition and proof. Use this as template to answer the question following it. Definition: A function f defined on the interval [a, b] will be said to be locally constant if for every x [a, b] there is some 8 >0 and some c, both depending on x, such that = if x =a then f(2)=c for all z [a, a +8) if x=b then f(2) =c for all z (6-0,6] if a< x 0 and some c such that f(z) =c for all z (a, a +8) in the case that w=a = f(z) =c for all z (w - 0,w+d) in the case that a a +8> a because w is an upper bound for S. This contradicts that a =w. To get a contradiction in the second case first note that since w is the least upper bound for S and w-s0 and some c such that f(z) = c for all z (6 - 8,6]. Now the argument proceeds as before. Since b is the least upper bound for S and 6-8 0 and some A and B, all three depending on x, such that . if x =a then f(x) = Az + B for all z [a, a +8) if x=b then f(z) = Az + B for all z (6 - 8,6] if a< x