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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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