Question

Solve the inequality by using the graph of the function.

Solve $f\left(x\right)\le 0$, where

$f\left(x\right)=-2(x+2)(x-2{)}^3$

Short answer

The solution of the inequality is $(-\infty ,-2]\cup [2,\infty )$.

Step-by-step solution

Step 1. Given Information 

We are given a function,

$f\left(x\right)=-2(x+2)(x-2{)}^3$

Step 2. Graphing the function  

The graph of the function is as follows,

Step 3. Solve the inequality  

As seen from the graph, $f\left(x\right)\le 0$for the interval $(-\infty ,-2]\cup [2,\infty )$.

Hence the solution is $(-\infty ,-2]\cup [2,\infty )$.