x A family of super-exponential functions? Let f(x) = (a? +x) ?, wher ? e ? > 0. a.? What is the dom ? ain of f ? (in te?rms of ?a)? b.? Describe the end be ? havior of f ? (near the boundary of its doma ? in or a? s ??x? ? ? ? ). ? c.? Compute ?f?.? Then? graph ? ?f and f? ? for ?a = 0.5, 1, 2, 3. ? d.? Show that ?f has a single local minimu?m at the point ?z that satisfies ? ? ? ? (?? + ?a)ln (?z + ?a)+ ?z = 0. ? e.? Describe how z ? [found in? part (d)] varies as ?a increases. Describe how f(z)varies as ?a increases.

Solution 76RE Step 1 In this problem we are given that f(x) = (a+x) where a > 0. We have to find the domain of f in terms of a and we have to explain the end behavior of f near the boundary. Then we need to find f and we need to draw the graph of f and f . Then we have to show that f has only one local minimum at the point z that satisfies the given condition.