Using the power rule for differentiation, the first derivative of
[tex]f(x) = -x^{\frac12}[/tex]
is
[tex]f'(x) = -\dfrac12 \cdot x^{\frac12-1} = -\dfrac12 x^{-\frac12}[/tex]
and the second derivative is
[tex]f''(x) = -\dfrac12 \cdot \left(-\dfrac12 \cdot x^{-\frac12 - 1}\right) = \dfrac14 x^{-\frac32}[/tex]
which makes E the correct choice.
