Question

The function m(x)= (x+3)/(x-2 on the interval [0,5 does not have any absolute extreme values. Does this contradict the Extreme Value Theorem?

Answer 1

No, Look at x-2 in the denominator

Answer 2

so it does not contradict the theorem meaning or it does since it does not have a max or min point.

Answer 3

The function must be continuous on the whole interval. Is yours continuous?

Answer 4

I belive so

Answer 5

No it is not continuous at x=2. Why?

Answer 6

since it is continuous over x=2 not at x=2

Answer 7

The denominator is zero at x=2 and the numerator is not.

Answer 8

Since the function is not continuous. It does not have to have a max or min on the interval [0,5]

Answer 9

The extreme value theorem is about continuous function. So the Theorem is not violated

Answer 10

ah I see, so since the denominator is zero at x=2 and the numerator is not, that makes the function not continues which will not produce any max or min within the intervals, correct?

Answer 11

Yes

Answer 12

that does not make any sense, if the theorem is about continues function and the function i have is not continuos, how can the theorem not be violated?

Answer 13

*continuos

Answer 14

The theorem might not be true if the function is not continuous. So for you function, the theorem does not apply, so there is no contradiction. That should be your answer.

Answer 15

oh okay well thank you for all of your help!