Solve the given inequalities graphically by using a calculator. See Example 8. Round all decimals to the nearest hundredth.

x³ − x > 2

Data from Example 8

Use a calculator to solve the inequality x³ > x² − 3. Finding the equivalent inequality with zero on the right, we have x³ − x² + 3 > 0. On the calculator, we then let y₁ = x³ − x² + 3 and graph this function, which is shown in Fig. 17.27.

Using the zero feature, we find that the zero of the function is approximately x = −1.17. Because we want values of x that correspond to positive values of y, we see that the solution is x > −1.17.

NORMAL FLOAT AUTO REAL DEGREE MP CALC ZERO Y1=X-X+3 Zero X=-1.174559 Y=0 Fig. 17.27