Question

Solve the inequality by using the graph of the function.

Solve$f\left(x\right)<0$, where$f\left(x\right)=x^2(x-3)$

Short answer

The solution of the inequality is$(-\infty ,0)\cup (0,3)$.

Step-by-step solution

Step 1. Graph the function

The graph of the function $f\left(x\right)=x^2(x-3)$is given as

Step 2. Solve the inequality

To find the solution of $f\left(x\right)<0$, we need to find the values of x for which the graph is below the x axis.

From the graph, we can see that for $x<3$ the graph is below the x axis. But at $x=0$, the function value is equal to$0$.

So the solution is given as $(-\infty ,0)\cup (0,3)$.