1. intermediate value theorem

Let be a continuous function such that and .

Using the Intermediate Value Theorem classify the following statements as:

( A ) Always true
( B ) Never True, or
( C ) True in some cases; False in others.

1. f(0)=0

2. For some c , where , .

thank you

2. Originally Posted by mybrohshi5
Let be a continuous function such that and .

Using the Intermediate Value Theorem classify the following statements as:

( A ) Always true
( B ) Never True, or
( C ) True in some cases; False in others.

1. f(0)=0

2. For some c , where , .

thank you

The assertion that the intermediate value theorem makes is a very intuitive concept.

What do you not understand about it? If you understand the theorem itself, these questions become obvious. Tell what the problem is, and I will help you.

3. I have the intermediate value theorem right here in front of me and i have read over it multiple times but i guess i dont get it.

for number 1 i thought it was A and for 2 i thought it was C but both of those are wrong and i dont understand why.

i thought 1 was A because i found N to be 0 so f(c)=N so f(0)=0 seemed to sound correct to me so i thought it was always true

i thought 2 was C because yes 0 is between those numbers but other numbers could be between those two numbers too.

thank you

4. Originally Posted by mybrohshi5
I have the intermediate value theorem right here in front of me and i have read over it multiple times but i guess i dont get it.

for number 1 i thought it was A and for 2 i thought it was C but both of those are wrong and i dont understand why.

i thought 1 was A because i found N to be 0 so f(c)=N so f(0)=0 seemed to sound correct to me so i thought it was always true

i thought 2 was C because yes 0 is between those numbers but other numbers could be between those two numbers too.

thank you

Ok Ok... Forget all of the formal crap that your book is shoving down your throat right now. In your mind visualize a a graph of a function. Now, this function is a smooth curve that starts at -1 on the y axis to and goes to +1 on the y axis.

So, think about it...Does this curve - if it is unbroken - have to pass through 0 to go from -1 to 1?

Or better yet: On a sheet of graphing paper, put two points on the page. Put one at (-8,-1) and the other at (8,1). Now here's the chalenge: Without lifting your pencil from the paper, see if you can draw a curve from (-8,-1) to (8,1) and not cross the x axis. It's impossible! this is what the IVT says!

5. thank you =)

6. Originally Posted by mybrohshi5
thank you =)
Are you certain that you've got it? I don't want you to leave here with any shadow of doubt.

7. If the answer to the question "Does f pass through the x-axis (that is, does f equal zero) at some point on the interval?" is "yes", then the second consideration (which is the first exercise) is "Must the x-value for that pss-through point necessarily be zero itself?"

8. Originally Posted by mybrohshi5
I have the intermediate value theorem right here in front of me and i have read over it multiple times but i guess i dont get it.

for number 1 i thought it was A and for 2 i thought it was C but both of those are wrong and i dont understand why.

i thought 1 was A because i found N to be 0 so f(c)=N so f(0)=0 seemed to sound correct to me so i thought it was always true

i thought 2 was C because yes 0 is between those numbers but other numbers could be between those two numbers too.

thank you