# Thread: function help

1. ## algebra and trigonometry with analytic geometry problem

The table shows several value of the function f(x)=-x^3+x^2-x+2. Complete the missing values in his table, and then use these values and the intermediate value theorem to determine (an) interval(s) where the function must have a zero.

table
x -2 -1 0 1 2
f(x) 16 -4
My answer is (-infty,0) u (2,infty), but I think that I'm wrong. thanks for any help.

2. Originally Posted by kwtolley
The table shows several value of the function f(x)=-x^3+x^2-x+2. Complete the missing values in his table, and then use these values and the intermediate value theorem to determine (an) interval(s) where the function must have a zero.

table
x -2 -1 0 1 2
f(x) 16 -4
My answer is (-infty,0) u (2,infty), but I think that I'm wrong. thanks for any help.
Fill in the table:

$\displaystyle \begin{array}{c|ccccc} {x}& {-2}&{-1}&{0}&{1}&{2}\\ {f(x)}& {16}&{5}&{2}&{1}&{-4} \end{array}$

Now as $\displaystyle x \to -\infty,\ f(x) \to +\infty$, and $\displaystyle x \to +\infty,\ f(x) \to -\infty$, we have no evidence for a zero for $\displaystyle x<-2$, or $\displaystyle x>2$.

Now $\displaystyle f(x)$ changes sign in $\displaystyle (1,2)$. Hence we conclude from the intermediate value theorem (and the continuity of $\displaystyle f(x)$) that $\displaystyle f(x)$ has a root in this interval.

RonL

3. ## table messed up on me sorry

redo of the table

x -2 -1 0 1 2
f(x) 16 _ _ _ -4