Chapter 11.3, Problem 4MRE

To determine

To calculate:

Given inequality and graph the solution.

Answer to Problem 4MRE

The solution of the inequality is $-2<x<0$ or $x>2$ .

Explanation of Solution

Given information:

Equation:

  $x^3>4x$

Calculation:

Consider the equation $x^3>4x$

Now solve the critical parts of the inequality,

  $\begin{array}{l}{x}^3=4x\\ x^3-4x=4x-4x\\ x^3-4x=0\\ x\left(x+2\right)\left(x-2\right)=0\\ x=0,x+2=0,x-2=0\\ x=0,x=-2,x=2\end{array}$

Now check the interval in between critical points.

  $\begin{array}{l}x<-2\\ -2<x<0\\ 0<x<2\\ x>2\end{array}$

The answer is $-2<x<0$ or $x>2$ .

The following graph shoes the equation $x^3>4x$ .