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Consider the function f : R → R defined by f(x) = ( 5 + sin...

Consider the function f : R → R defined by f(x) = ( 5 + sin x if x < 0, x + cos x + 4 if x ≥ 0. Show that the function f is differentiable for all x ∈ R. Compute the derivative f' . Show that f ' is continuous at x = 0. Show that f ' is not differentiable at x = 0. (In this question you may assume that all polynomial and trigonometric functions are differentiable anywhere they are defined, with their well-known derivatives.)

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