Question

I am so confused on what to do with fractions.

Answer 1

Using the power rule for differentiation, the first derivative of

$f(x) = -x^{\frac12}$

is

$f'(x) = -\dfrac12 \cdot x^{\frac12-1} = -\dfrac12 x^{-\frac12}$

and the second derivative is

$f''(x) = -\dfrac12 \cdot \left(-\dfrac12 \cdot x^{-\frac12 - 1}\right) = \dfrac14 x^{-\frac32}$

which makes E the correct choice.