Solve each inequality in Exercises 86–91 using a graphing utility. x^3 + x^2 - 4x - 4 > 0

Key Concepts

Inequalities

Inequalities express a relationship where one side is not equal to the other, often using symbols like '>', '<', '≥', or '≤'. In this case, the inequality x^3 + x^2 - 4x - 4 > 0 indicates that we are looking for values of x that make the expression positive. Understanding how to manipulate and solve inequalities is crucial for finding the solution set.

Graphing Utility

A graphing utility is a software or tool that allows users to visualize mathematical functions and inequalities. By inputting the inequality into the graphing utility, one can observe where the graph of the function is above the x-axis, which corresponds to the solution of the inequality. Familiarity with using these tools is essential for efficiently solving complex inequalities.

Polynomial Functions

Polynomial functions are expressions that involve variables raised to whole number powers, combined using addition, subtraction, and multiplication. The given inequality involves a cubic polynomial, which can have up to three real roots. Understanding the behavior of polynomial functions, including their end behavior and critical points, is vital for determining where the function is positive or negative.