- #1
Glissando
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Homework Statement
Find the relative extrema of the following function f(x) = (a-x)/(x2-a2)
where a is a constant, a>0
Homework Equations
Derivative of f(x), zeroes, quadratic formula
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
Quadratic formula:
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