Consider the following functions:1. \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{{\rm{x}}}{\rm{\;\;if\;\;x}} \ne 0}\\ {0{\rm{\;\;if\;\;x}} = 0} \end{array}} \right.\)2. \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {2{\rm{x}} + 5{\rm{\;\;if\;\;x}} > 0}\\ {{{\rm{x}}^2} + 2{\rm{x}} + 5{\rm{\;\;if\;\;x}} \le 0} \end{array}} \right.\)Which of the above functions is/are derivable at x = 0?

Consider the following functions:1. \({\rm{f}}\left( {\rm{x}} \right)

1.	Consider the following functions:1. \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{{20}{c}} {\frac{1}{{\rm{x}}}{\rm{\;\;if\;\;x}} \ne 0}\\ {0{\rm{\;\;if\;\;x}} = 0} \end{array}} \right.\)2. \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{{20}{c}} {2{\rm{x}} + 5{\rm{\;\;if\;\;x}} > 0}\\ {{{\rm{x}}^2} + 2{\rm{x}} + 5{\rm{\;\;if\;\;x}} \le 0} \end{array}} \right.\)Which of the above functions is/are derivable at x = 0?
A.	1 only
B.	2 only
C.	Both 1 and 2
D.	Neither 1 nor 2
Answer» C. Both 1 and 2

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