+845 
ONLY 5C PLEASE
ok so for this question i have showed one of the coordinate is (1,0) what im struggling with is the other stationary point.
i simplified the rational function into (3x^2 - 6x +3)/(2x^2 + 6)
then i differentiated the numerator into 6x-6
using the quotent rule i have
(6x-6)*(2x^2+6) - (3x^2 - 6x +30) (6x -6)
i expanded and simplified them into
-6x^3 + 12x^2 - 18x -18
what should i do from here?
+128475 We don't need to worry about the denominator with the quotient rule
Remember that the quotient rule is .... (f / g)' = [f' g - f g'] / [ g^2 ]
f = 3(x - 1)^2 = 3x^2 - 6x + 3
g = 2x^2 + 6
So....
The numerator is
(6x - 6)(2x^2 + 6) - (3x^2 - 6x + 3) (4x) = 0
6 ( x - 1) * 2 (x^2 + 3) - 3(x - 1)^2(4x) = 0
12(x - 1) (x^2 + 3) - 12x(x - 1)^2 = 0
12(x - 1) [ (x^2 + 3) - ( x(x - 1) ] = 0
12 (x - 1) [ x^2 + 3 - x^2 + x] = 0
12(x - 1) (x + 3 ) = 0
Setting both factors to 0 and solving for x produces the two stationary x coordinates of x = 1 and x = - 3
And f(-3) = 2
So....the other stationary point is (-3, 2)
