Question

the inequality $-x^2 - 6 < 0$ has 0 critical points. complete
what is the solution set of $-x^2 - 6 < 0$?
$\varnothing$
${x | x \in \mathbb{r}}$
done

Explanation:

Step1: Analyze the inequality

We have the inequality \(-x^2 - 6 < 0\). Let's rewrite it as \(x^2+ 6>0\) (by multiplying both sides by - 1, and reversing the inequality sign).

Step2: Analyze the expression \(x^2 + 6\)

For any real number \(x\), the square of a real number \(x^2\geq0\). So \(x^2 + 6=x^2+0 + 6\). Since \(x^2\geq0\), then \(x^2 + 6\geq6>0\) for all real numbers \(x\). This means that the inequality \(x^2 + 6>0\) (or equivalently \(-x^2-6 < 0\)) is true for all real numbers \(x\).

Answer:

\(\{x|x\in\mathbb{R}\}\)