Question

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers.

Answer 1

As a first step we are going to evaluate f(-1) and f(0):

`\begin{gathered} f(x)=-4x^3-9x^2+2x+6 \\ f(-1)=-4(-1)^3-9(-1)^2+2(-1)+6 \\ f(-1)=4-9-2+6 \\ f(-1)=-1 \end{gathered}`
`\begin{gathered} f(0)=-4(0)^3-9(0)^2+2(0)+6 \\ f(0)=6 \end{gathered}`

The answer is C between f(-1) and f(0)=6 there is a real zero