Answer
The position where the power is maximum can be found by differentiating $P$ with
respect to $x$ , setting $d P / d x=0$ :
$$
\frac{d P}{d x}=\frac{k^{2}\left(x_{i}^{2}-2 x^{2}\right)}{\sqrt{\frac{k\left(x_{i}^{2}-2 x^{2}\right)}{m}}}=0
$$
which gives $x=\frac{x_{i}}{\sqrt{2}}=\frac{(0.300 \mathrm{m})}{\sqrt{2}}=0.212 \mathrm{m}$
Work Step by Step
The position where the power is maximum can be found by differentiating $P$ with
respect to $x$ , setting $d P / d x=0$ :
$$
\frac{d P}{d x}=\frac{k^{2}\left(x_{i}^{2}-2 x^{2}\right)}{\sqrt{\frac{k\left(x_{i}^{2}-2 x^{2}\right)}{m}}}=0
$$
which gives $x=\frac{x_{i}}{\sqrt{2}}=\frac{(0.300 \mathrm{m})}{\sqrt{2}}=0.212 \mathrm{m}$
