# Math Help - Maxima and Minima

1. ## Maxima and Minima

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

2. simplify the function-> $1+(6/(x-3+1/x))$
you will see that when x=1,it attains max and when x=-1,it attains min.

3. How do you simplify the above expression to 1+(6/(x-3+1/x)) ?

4. 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

$\frac{-1+\frac{1}{x^2}}{(x-3+\frac{1}{x})^2}$

the root of the numerator {-1,1} and the root denominator

$\frac{3-+\sqrt{5}}{2}$

but the denominator is always positive
look at this