Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Need some help on a Calculus problem.

It says:

Prove that if a != b then f(x) = 1 \ ((x-a)(x-b)) is symmetric about x = (a+b)/2

I have no idea how to go on about this problem. I took the derivative of f(x) and found out that x = (a+b)/2 is when the derivative is equal to zero. But what does that tell me?

Thanks.

Last edited by LuisRodg (2007-11-12 09:43:41)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Need some help on a Calculus problem.

f(x) is symmetrical about the line x = k if f(k+x) = f(k−x). That’s what it means.

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Need some help on a Calculus problem.

so following on, this is how i work it out

Last edited by luca-deltodesco (2007-11-12 10:40:32)

---

The Beginning Of All Things To End.
The End Of All Things To Come.

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Need some help on a Calculus problem.

Ok got it. I just never learned that a function is symmetrical if f(k+x)=f(k-x)

What about this:

Show that y=x+3 is an oblique asymptote of the graph of f(x)=x^2/(x-3)

I dont even know what an oblique asymptote is. I guess my problem lies in pre-calc and not calculus itself.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Need some help on a Calculus problem.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Need some help on a Calculus problem.

Another way to do the first question.

Now you can easily see that

.

Last edited by JaneFairfax (2007-11-13 01:46:13)