(b) Consider the function f : [-3, 2] - R defined by x2ex if x E [-3, 1] f (x) = e2 - x if x E (1, 2] You may take for granted that the limits f(1 + e) - f(1) f(1 + e) - f(1) lime-+0- and lime-+0+ E E are not equal, which implies that f is not differentiable at x = 1. (i) Explain why the existence of at least one global maximum of f on [-3, 2] is guaranteed. (ii) Express the domain [-3, 2] of f as a union /1 U /2 of two disjoint intervals /1, /2 with the property that f is differentiable in the interior of each interval. (ii) Hence identify the global maxima (or maximum if there is only one) of f on [-3, 2]