Question

Hello! It’s RoseI need help solving this prep guide problem in calc

Answer 1

Given:

`f(x)=-x^3-x^2+4x+9`

we will substitute with x = 0, 1, 2, 3, 4

the zero of the function will be when the sign of f(x) is changed from (+) to (-) or vice versa

so,

`\begin{gathered} x=0\rightarrow f(x)=9 \\ x=1\rightarrow f(x)=11 \\ x=2\rightarrow f(x)=5 \\ x=3\rightarrow f(x)=-15 \\ x=4\rightarrow f(x)=-55 \end{gathered}`

Now, note when x = 2, f(x) is positive and when x = 3, f(x) is negative

This means between x = 2 and x = 3, the function f(x) will intersect with the x-axis which will give a zero for the function

so, the function has a zero between x = 2 and 3

so, the answer will be option: 2 and 3