Answer: intercepts \(x=-5,-2,\frac12\), \(y=2\); \(x\leq -5\) or \(-2\leq x\leq \frac12\).

We start with the main method. Use the measurements and relationships shown in the diagram, then translate them into algebraic or trigonometric equations. Use the graph to identify the intervals where the curve lies above or below the required level.

The \(x\)-intercepts occur when one of the factors is zero:

\(x+2=0,\quad 2x-1=0,\quad x+5=0.\)

So the graph cuts the \(x\)-axis at

\(x=-2,\quad x=\frac12,\quad x=-5.\)

For the \(y\)-intercept, put \(x=0\):

\(y=-\frac15(2)(-1)(5)=2.\)

The leading term is

\(-\frac15(x)(2x)(x)=-\frac25x^3.\)

So the cubic rises on the left and falls on the right.

Using the sign of the cubic across the three roots, the graph is on or above the \(x\)-axis when

\(x\leq -5\quad\text{or}\quad -2\leq x\leq \frac12.\)

This completes the solution and gives the required result.