Problem

A function is defined by $f(x) = \frac{4}{x^3} - \frac{3}{x} + 2$ for $x \ne 0$. The graph of $y = f(x)$ is shown in the diagram.

(a) Find the set of values of $x$ for which $f(x)$ is decreasing.

(b) A triangle is bounded by the $y$-axis, the normal to the curve at the point where $x = 1$ and the tangent to the curve at the point where $x = -1$.

Find the area of the triangle. Give your answer correct to $3$ significant figures.