function help

**kwtolley** · June 25th 2006, 02:36 AM

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.

**CaptainBlack** · June 25th 2006, 03:17 AM

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:

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

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

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

RonL

**kwtolley** · June 25th 2006, 03:48 AM

redo of the table

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

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algebra and trigonometry with analytic geometry problem

table messed up on me sorry

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