For the piecewise function f(x) = {x + 1 if x ≥ 0 and x +2 if x < 0

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For the piecewise function f(x) = {x + 1 if x ≥ 0 and x +2 if x < 0

[From: ] [author: ] [Date: 11-10-22] [Hit: ]

explain why.I really am getting two different answers: graphically, the graph indicates a discontinuity while the left-hand and the right-hand limits are both equal. Any help?-f(0) does not exist because the function is discontinuous at x = 0. For the derivative to exist at some point in the domain of the function,......

Does f'(0) exist? If it does, find its value. If it does not, explain why.

I really am getting two different answers: graphically, the graph indicates a discontinuity while the left-hand and the right-hand limits are both equal. Any help?

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f'(0) does not exist because the function is discontinuous at x = 0. For the derivative to exist at some point in the domain of the function, the function must be continuous at that point. This function is discontinuous at x = 0 and is, therefore, not differentiable at x = 0.

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