SOLUTION: The table shows several value of the function f(x)= -x^3+x^2-x+2. Complete the missing values in this table, and then use these values and the intermediate vaule theorem to determ

Question 43599This question is from textbook Algebra and trigonometry with analytic geometry
: The table shows several value of the function f(x)= -x^3+x^2-x+2. Complete the missing values in this table, and then use these values and the intermediate vaule theorem to determine (an) interval(s) where the function must have zero.
x -2 -1 0 1 2
f(x) 16 -4
My answer is (0,1) u (2,infty) but unsure. thanks as always for the help. This question is from textbook Algebra and trigonometry with analytic geometry

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x)= -x^3+x^2-x+2.
x -2 -1 0 1 2
f(x) 16 -4
Your f(-1), f(0), and f(1) are all positive.
Your f(2) is negative.
Since the function is continuous in the interval x=1 to x=2
The graph must cross the x-axis to get from + to -
Therefore there must be a zero between x=1 and x=2.
Cheers,
Stan H.
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