Can You Solve for a+b/2 in the Continuity Problem f(x)=((x-a)^2)*((x-b)^2) + x?

[fastblue]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Dick]

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

 

[fastblue]

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

Have no idea...

 

[Dick]

Have no idea...

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

 

[fastblue]

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

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

 

[Dick]

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

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

 

[fastblue]

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

 

[fastblue]

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

 

[fastblue]

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

 

[Dick]

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

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

 

[fastblue]

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

 

[fastblue]

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

 

[Dick]

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

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

 

[fastblue]

0 I guess?

 

[fastblue]

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

 

[Dick]

0 I guess?

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.

 

[fastblue]

Sorry still don't get the relationship thing between a+b/2, can you explain further