3. Let f(x) = c.(x-4)+2 if 0 ≤x≤4 if x > 4 where c denotes a real constant. (a) Show that lim f(x) = lim f (x) and that fe is continuous at x = 4 for any real c. x->4+ X-4 (b) Sketch the curves y = f(x) on separate graphs for c=0, c=1, and c= -1. (c) Determine the unique value of c for which fe is differentiable at x = 4, i.e., find c so that (f)+ (4) = (f)'_ (4).

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A:

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