Question: Define a function f : R R by f(x) = x 3 x 0 and -x 3 x < 0 (a) Show that f is

Define a function f : R R by f(x) = x³ x 0 and -x³ x < 0

(a) Show that f is continuous. (b) Show that f is differentiable, and calculate f'(x). (c) Is f' continuous? Explain why or why not. (d) For which values of x does f''(x) exist? For those values of x, find f''(x).

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