Question

Select the correct choice below and fill in the answer

Answer 1

Step 1:

Write the function

`g(x)=x^5-16x^3`

Step 2:

Write an inequality equation where g(x) > 0

`\begin{gathered} x^5-16x^3\text{ > 0} \\ \text{Factorize the left hand side of the equation} \\ x^3(x^2\text{ - 16) > 0} \\ x^3(x\text{ - 4)(x + 4) > 0} \end{gathered}`

Step 3:

Identify the intervals

- 4 < x < 0 or x > 4

`\text{Answer in interval notation: }(\text{ - 4 , 0 ) }\cup\text{ ( 4 , }\infty\text{ )}`