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If {:(f(x)=1+x," ""when"x ne 1),(=1," ""...

If `{:(f(x)=1+x," ""when"x ne 1),(=1," ""when"0lexle1),(2x^(2)+4x+5, " ""when"xgt1):}`
find f'(x) for real x . Does `lim_(x to 0)` f'(x) exist ?

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The correct Answer is:
`{:(f(x)=1," ""when"x lt 1),(=0," ""when"0ltxlt1),(=4(x+1), " ""when"xgt1):}`
`underset(x = to 0) lim ` f'(x) does not exist
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