Chapter 1.9, Problem 70E

To determine

Tofind:the solution of the interval on x-axis in which curve lies under x-axis.

Answer to Problem 70E

The solution is interval on x-axis in which the curve lies under x-axis

  $x\ge 1\text{ and x}\le \text{-1}$ .

Explanation of Solution

Given:

  ${\text{x}}^2\left({\text{x}}^2\text{-1}\right)\ge \text{0}$ .

Concept used:

The lowest value or the roots is taken as minimum point where the solution exist.

The highest value or the roots is taken as maximum point where the solution exist.

The graph can predict the solution below x-axis.

Calculation:

Required:

  ${\text{x}}^2\left({\text{x}}^2\text{-1}\right)\ge \text{0}$ .

Solve the graphically the inequality

  $x\ge 1\text{ and x}\le \text{-1}$ .

The solution is interval on x-axis in which the curve lies under x-axis.

  $x\ge 1\text{ and x}\le \text{-1}$ .

Graph of ${\text{x}}^2\left({\text{x}}^2\text{-1}\right)$ :

  

Hence, the solution is interval on x-axis in which the curve lies under x-axis

  $x\ge 1\text{ and x}\le \text{-1}$ .