A function is defined in (0, ∞) by \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {1 - {{\rm{x}}^2}{\rm{\;for\;}}0 < {\rm{x}} \le 1}\\ {{\rm{In\;x\;for\;}}1 < {\rm{x}} \le 2}\\ {{\rm{In\;}}2 - 1 + 0.5{\rm{x\;for\;}}2 < {\rm{x}} < \infty } \end{array}} \right.\)Which one of the following is correct in respect of the derivative of the function, i.e. f’(x)?

A function is defined in (0, ∞) by \({\rm{f}}\left( {\rm{x}} \right)

1.	A function is defined in (0, ∞) by \({\rm{f}}\left( {\rm{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {1 - {{\rm{x}}^2}{\rm{\;for\;}}0 < {\rm{x}} \le 1}\\ {{\rm{In\;x\;for\;}}1 < {\rm{x}} \le 2}\\ {{\rm{In\;}}2 - 1 + 0.5{\rm{x\;for\;}}2 < {\rm{x}} < \infty } \end{array}} \right.\)Which one of the following is correct in respect of the derivative of the function, i.e. f’(x)?
A.	f’(x) = 2x for 0 < x ≤ 1
B.	f’(x) = -2x for 0 < x ≤ 1
C.	f’(x) = -2x for 0 < x < 1
D.	f’(x) = 0 for 0 < x < ∞
Answer» C. f’(x) = -2x for 0 < x < 1

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