Nonlinear inequality

Definition

A nonlinear inequality is an inequality that involves a nonlinear function, such as quadratic, cubic, or higher-degree polynomials. These inequalities can be solved by finding the regions where the function is above or below a certain value.

5 Must Know Facts For Your Next Test

1. The solution to a nonlinear inequality may consist of multiple intervals.
2. Graphing the function can help visualize the solution regions for the inequality.
3. Nonlinear inequalities often require factoring or using the quadratic formula to find critical points.
4. Inequalities involving absolute values may need to be split into separate cases for solving.
5. Test points from different intervals can confirm which regions satisfy the inequality.

Review Questions

• What steps are involved in solving a quadratic inequality?
• How can graphing a nonlinear function help solve its corresponding inequality?
• When solving an inequality involving absolute values, why do you need to consider separate cases?

Related terms

Quadratic Inequality: An inequality that involves a quadratic function, typically in the form $ax^2 + bx + c \geq 0$ or $ax^2 + bx + c \leq 0$.

System of Nonlinear Equations: A set of equations in which at least one equation is nonlinear and they are solved simultaneously.

Critical Points:

Values of the variable where the derivative is zero or undefined, often used to determine intervals for testing inequalities.