Question 65567: There are several values of the function f(x)=-x^3+x^2-x+2. Complete the missing values., and then use these values and the intermediate value theorem to determine (an) interval(s) where the function must have a zero.
x: -2,-1,0,1,2; f(x): 16,...,...,...,-4
This was shown as a table where "x" was over f(x) and we have to find the missing variables and then solve. I would really appreciate some help.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! f(x)=-x^3+x^2-x+2
Complete the missing values., and then use these values and the intermediate value theorem to determine (an) interval(s) where the function must have a zero.
x: -2,-1,0,1,2; f(x): 16,...,...,...,-4
------------
f(-2)=16
f(-2)=-(-1)^3+(-1)^2-(-2)+2=-1+1+2+2=4
f(0)=2
f(1)=-1+1-1+2=1
f(2)=-4
The change in sign occurs between x=1 and x=2 so there must
be a zero on the interval (1,2)
Cheers,
Stan H.
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