1. ## help with proof please

How do I prove that that a function f must have a zero on a given interval [a,b]

thanks,
D.

2. Originally Posted by dboyd435
How do I prove that that a function f must have a zero on a given interval [a,b]
One cannot prove a statement that is false.
As written the statement is false. Please review and correct your post.
Better yet, post the actual problem using the exact wording.

3. oh, how was the first statement wrong?

"prove that f must have a zero on the interval [a,b]. Make sure to give a clear explanation with your proof."

Thanks.

4. As Plato pointed out, this statement is false.

Perhaps you're looking at a continuous function which has both signs (so positive and negative) on a given interval [a,b]?

5. Originally Posted by TD!
As Plato pointed out, this statement is false.

Perhaps you're looking at a continuous function which has both signs (so positive and negative) on a given interval [a,b]?
maybe I should just post the actual function... I think just realized what you have been trying to say.

the interval [0,3] and the function being f(x)= 2x^3 - 9x^2 + 12x - 7

6. You could explicitly try to find the zero, but that would be "messy" here. My guess is that you've seen the theorem I was referring to in my last post (a continuous function that changes sign in an interval, has a zero in that interval). Can you check that your function is indeed positive and negative on [0,3]?

7. could I say that because f changes sign between x=2 and x=3 f must have a zero on the interval [0,3] because f must intersect the x-axis in order to chance from (2,-3) to (3,2)

8. Well, I think that's the point. Have you seen that theorem?

9. probably, I just can not remember it.