# Homework Help: Find the relative extrema

1. Jun 16, 2011

### Glissando

1. The problem statement, all variables and given/known data
Find the relative extrema of the following function f(x) = (a-x)/(x2-a2)
where a is a constant, a>0

2. Relevant equations
Derivative of f(x), zeroes, quadratic formula

3. The attempt at a solution

I think I just screwed a small step in there because my answer doesn't work out (it's supposed to be a(1 + sqrt2) and a(1 - sqrt2)

f'(x) = [(x2+a2)(-1) - (2x)(a-x)]/(x2+a2)2

0 = -x2 - a2 - 2xa + 2x2

0 = x2 - 2xa - a2

x = [-b +/- sqrt(b2 - 4ac)]/(2a)

x = {2xa +/- sqrt[(-2xa)2 - 4(x2)(-a2)]}/(2x2)

x = [2xa +/- sqrt(4x2a2 + 4x2a2)]/(2x2)

x = [2xa +/- sqrt(8x2a2)]/(2x2)

x = [2xa +/- 2sqrt(2)xa]/(2x2)

x = 2xa(1 +/- sqrt2)/(2x2)

x = a(1 +/- sqrt2)/x

): How do I get rid of the x? If you cancel it doesn't the left side become 1?

Thank you for your help! <3

2. Jun 16, 2011

### Dick

It looks like you meant to say f(x)=(a-x)/(x^2+a^2) in the problem statement. So, yes, you want to solve 0=x^2-2ax-a^2. When you use the quadratic formula you put 'a'=1, 'b'=(-2a) and 'c'=(-a^2). I put quotes around the variables in the quadratic formula so as not to confuse them with the a in the problem. Notice none of them have an x in it.

3. Jun 16, 2011

### Glissando

WOW that made all the difference! Thank you so much (:!!