1 of 8 0-day streak

Solve a cubic inequality

Question 1 of 8

No calculator

Consider the following cubic inequality for real x

-\left(x + \frac{1}{2}\right)^{3} \le 0

Use exact values. Let F(x) denote the left side after the inequality is written in zero form. Compare F(x) with zero, find and order the critical roots, then complete the sign chart

(a)2 marks

Record the exact critical roots and state how often each factor occurs

\(r_{1}\) \(m_{1}\)

(b)1 mark

Choose the sign for the interval \(x<-\frac{1}{2}\)?

positive on this interval

negative on this interval

Choose the sign for the interval \(x>-\frac{1}{2}\)?

positive on this interval

negative on this interval

(d)1 mark

State the solution set using the critical roots and the correct brackets

x\in \left[-\frac{1}{2},\ \infty\right)

x\in \left(-\infty,\ -\frac{1}{2}\right]

x\in \left\{-\frac{1}{2}\right\}

x\in \left(-\frac{1}{2},\ \infty\right)