# Solving for continutity

1. Sep 23, 2009

### fastblue

1. The problem statement, all variables and given/known data

Show the problem f(x)=((x-a)^2)*((x-b)^2) + x take on a value of a+b/2
for some x?

2. Relevant equations

3. The attempt at a solution

2. Sep 23, 2009

### Dick

What are f(a) and f(b)?? Can you think of a theorem that might apply??

3. Sep 23, 2009

### fastblue

Have no idea...

4. Sep 23, 2009

### Dick

What are f(a) and f(b)????? Work it out!!

5. Sep 23, 2009

### fastblue

How do I do that, can you show me.
Thanks

6. Sep 23, 2009

### Dick

Put 'a' in for 'x' into your expression for f(x). The result is f(a). What is it? Start DOING SOMETHING, ok?

7. Sep 23, 2009

### fastblue

ok, what does that do for you, as get two different answers

8. Sep 23, 2009

### fastblue

so that gives you (a-b)^2 + a and (b-a)^2 + b
so what do u do next.

9. Sep 23, 2009

### fastblue

a^2+b^2 - 2ab and b^2+a^2-2ab +b

10. Sep 23, 2009

### Dick

That's not right. Show me how you got those and I'll show you what you did wrong.

11. Sep 23, 2009

### fastblue

I just put in a for x and b for x, its obvious, what is wrong with it...?

12. Sep 23, 2009

### fastblue

Could you show me the reasoning, as have no clue how to do the problem, just spinning my wheels.

13. Sep 23, 2009

### Dick

f(a)=(a-a)^2*(a-b)^2+a. What's (a-a)^2?

14. Sep 23, 2009

### fastblue

0 I guess?

15. Sep 23, 2009

### fastblue

so how do you solve the remainder of the problem then??

16. Sep 23, 2009

### Dick

So what does that give for f(a) and f(b)? How are they related to (a+b)/2? To finish it get your book out and look for a theorem about continuous functions that might help. I'll give you a hint. The name of the theorem has the word 'intermediate' in it.

17. Sep 23, 2009

### fastblue

Sorry still dont get the relationship thing between a+b/2, can you explain further