SOLUTION: Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = -2x^4 + 2x^2 + 4; [-2, -1] a. f(-2) = 20 and f(-1) =

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Question 1060941: Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x) = -2x^4 + 2x^2 + 4; [-2, -1]
a. f(-2) = 20 and f(-1) = 5; no
b. f(-2) = -20 and f(-1) = 4; yes
c. f(-2) = 20 and f(-1) = -4; yes
d. f(-2) = -20 and f(-1) = -4; no

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
You EITHER know OR don't know the intermediate value theorem.

If you don't know (but still want to learn it), then learn it from the textbook or from the Internet.

If you know it, then complete this assignment on your own.

To facilitate you learning the intermediate value theorem, I copied and pasted its formulation below (from this Wikipedia article)

     In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, [a, b], as its domain, 
     takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.

     This has an important corollary: If a continuous function has values of opposite sign inside an interval, then it has a root in that interval.

So, what you need to do is to check the calculations/numbers and then to apply the theorem, which is quite easy.


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