Q) At what integral value of x will the function
(x^2 + 3x + 1)/(x^2 -3x+1) attains its maximum value?
Any help would be greatly appreciated.
Thanks,
Ashish
the critical points (3+5^1/2)/2 and (3-5^1/2)/2
since
(x^2 +3x+1)/(x^2 -3x+1)=(x^2-3x+1 +6x)/(x^2-3x+1) = 1+6x/(x^2-3x+1)
= 1+6(x-3+1/x)^-1= f(x)
f`(x) = -1 (1 -1/x^2)(x-3+1/x)^-2 = 0
$\displaystyle \frac{-1+\frac{1}{x^2}}{(x-3+\frac{1}{x})^2}$
the root of the numerator {-1,1} and the root denominator
$\displaystyle \frac{3-+\sqrt{5}}{2}$
but the denominator is always positive
look at this