Question

Solve the inequality by using the graph of the function.

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

role="math" localid="1646231564659" $f\left(x\right)=-\frac{1}{2}(x+4)(x-1{)}^3$

Short answer

The solution of the inequality is $(-\infty ,-4)\cup (1,\infty )$.

Step-by-step solution

Step 1. Given Information 

We are given a function,

$f\left(x\right)=-\frac{1}{2}(x+4)(x-1{)}^3$

Step 2. Graphing the function  

The graph of the function is as follows,

Step 3. Solve the inequality  

As seen from the graph, $f\left(x\right)<0$for the interval $(-\infty ,-4)\cup (1,\infty )$.

Hence the solution is $(-\infty ,-4)\cup (1,\infty )$.