Let

1. Show that the equation

   $$f^{\prime }(x)=0$$

   may be rearranged into the form

   $$x=\arccos (-\frac{1}{\sqrt{2x}})$$

2. Using a starting value of $x_0=2,$ find a fourth approximation, $x_3,$ for the location of one of the stationary points of the curve $y=f(x).$

3. By considering $f^{\prime }(x)$ at $x=x_3$ and $x=x_3\pm 0.001$ determine whether $x_3$ is an overestimate or an underestimate for the location of the stationary point.

4. Given that the stationary point is a turning point, state whether this is a maximum or a minimum point of the curve.

Find the value of $x_3$, rounded to $3$ decimal places.

If $x_3$ is an underestimate for the location of the stationary point, multiply this by $13$; otherwise multiply by $17$.

If the turning point is a minimum point, multiply this by $-1$; otherwise do nothing.

Give your answer below.