Jika \( \displaystyle f(x) = \frac{1}{x^2}-\frac{1}{x} + 1 \), maka \( \displaystyle f’ \left( \frac{1}{2} \right) = \cdots \)
- -20
- -16
- -12
- -8
- -4
(UMB 2008)
Pembahasan:
\begin{aligned} f(x) &= \frac{1}{x^2}-\frac{1}{x} + 1 \\[8pt] &= x^{-2}-x^{-1}+1 \\[8pt] f'(x) &= -2x^{-3}+x^{-2} \\[8pt] f' \left( \frac{1}{2} \right) &= -2\left( \frac{1}{2} \right)^{-3} + \left( \frac{1}{2} \right)^{-2} \\[8pt] &= -2 \left( 2^{-1} \right)^{-3} + \left( 2^{-1} \right)^{-2} \\[8pt] &= -2(2^3)+2^2 = -2 \cdot 8 + 4 \\[8pt] &= -16 + 4 = -12 \end{aligned}
Jawaban C.