Show that the function f(x) = |x - 2| is not differentiable at 2. We have if x 2 2 f(x) = |x - 21 = if x < 2. The right-hand limit is lim fx) – f(2) _ x - 2 x→2+ and the left-hand limit is lim x2- f(x) – f(2) – x - 2 Since these limits are not equal, f'(2) = lim 1 does not exist and f is not differentiable at 2. x – 2 X→2 Find a formula for f' and sketch its graph. if x > 2 f'(x) = if x < 2

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A: Topic :- limits

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