AP2) Prove that | sin æ – sin y| < |æ – y| _for all x, y E R. AP3) Prove that f(x) = |x|x(1-x) is differentiable on R. Find all relative extrema. AP4) Prove that f(x) = |x|x² satisfies f(0) = f' (0) ="f" (0) = 0, and yet fl" (0) does not exist. %3|

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