SOLUTION: I just got back a test I took in Pre-Calculus and the grade I got was ok. 93. I have a question though. There was this one question which I would like your opinion on. Eval

Question 457057: I just got back a test I took in Pre-Calculus and the grade I got was ok. 93.
I have a question though. There was this one question which I would like your opinion on.
Evaluate the function for the given values of a and b. Then use the intermediate value theorem to determine which of the statements below is true.
a=1 and b=2
f(x)= x^4-9x^3+20x^2+19x+29
The correct answer was (C), f(1) and f(2) have the same sign, therefore the intermediate value theorem CANNOT be used to determine whether f has a real zero between 1 and 2.
I obviously got it wrong, I answered (D), F(1) and F(2) have the same sign, therefore f does not have a real zero between 1 and 2.
(I worked my question right and got all the right signs and everything)
I guess what I'm really trying to ask is whether D could be considered a right answer or not as Im planning to go to my professor with the question as well and I would like to have some sort of valid argument.
So if you could point me in the right direction I would be very grateful. Thanks so much for your time.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
D is not correct because the fact that the two signs are the same does not automatically negate the existence of a zero between 1 and 2. There could still be a zero, but not necessarily. However, you cannot use the mean value theorem because the mean value theorem only guarantees f(x) values ranging from f(1) and f(2), in which zero is not included. Hence, C would be correct.
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