SOLUTION: Greetings, Any help with the following would be appreciated. 1. The table shows several values of the function f(x) = -x^3 + x^2 -x + 2. Complete the missing values in

Question 85220: Greetings,
Any help with the following would be appreciated.
1. The table shows several values 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 value theorem to determine (an) interval(s) where the function must have a zero.
x -2 , -1 , 0 , -1 , 2
f(x) 16 , ? , ? , ? , -4
Possible choices are:
(0, 1)
(1, 2)
(0, 1) ∪ (2, ∞)
(�∞, 0) ∪ (2, ∞)

Answer by scianci(186) (Show Source): You can put this solution on YOUR website!
You have f(-2) = 16 , f(-1) = 3 , f(0) = 2 , f(1) = 1 and f(2) = -4. Since f(x) changes sign from x = 1 to x = 2, by the Intermediate Value Theorem there must be a zero between 1 and 2. Tha answer is (1 , 2).
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