Question 1146032: Am I on the right track on this one?
For f (x) = x4 - 3x2 − 8, use the Intermediate Value Theorem to determine which interval(s) must contain a zero of f.
Work/Explanation required Answer. A,B, D
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
A. f(0)=(0)^4-3(0)^2-8=-8 f(1)= (1)^4-3(1)^2-8=-10
B. f(1)= (1)^4-3(1)^2-8=-10 f(2)= (2)^4-3(2)^2-8=-4
C. f(2)= (2)^4-3(2)^2-8=-4 f(3)= (3)^4-3(3)^2-8=46
D. f(3)= (3)^4-3(3)^2-8=46 f(4)= (4)^4-3(4)^2-8=200
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
I can't tell if you are on the right track, because I don't know what you are going to do with the calculations you have shown....
For the x values in the answer choices, the only change of sign in the function value is between x=2 and x=3. Therefore, for the intervals determined by the points given in the answer choices, the only interval that MUST contain a zero of the function is between 2 and 3.
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