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4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable...

4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable at x = 0 and f'(0) = g(0).

4b). Let f : (a,b) to R and p in (a,b). You may assume that f is differentiable on (a,b) and f ' is continuous at p. Show that f'(p) > 0 then there is delta > 0, such that f is strictly increasing on D(p,delta). Conclude that on D(p,delta) the function f has a differentiable inverse.

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