question on curve, points of inflection, stationary points and max and min points
For the function: y=2x^2/x^2-1
(i) Find all stationary points.
(ii) Find the intervals where y is increasing and the intervals where y is decreasing.
(iii) Find all local minima and local maxima.
(iv) Find all inflection points.
(v) Sketch the graph, indicating all maxima and minima, and all in
ection points.
Re: question on curve, points of inflection, stationary points and max and min points
First, start differentiating the function.
Re: question on curve, points of inflection, stationary points and max and min points
1st find -1})
putting 
gives (0,0) as stationary point
Now for x < 0, y is increasing and for x > 0, y is decreasing
apply second derivative test to find (0,0) as maxima
curve has no point of inflection
Re: question on curve, points of inflection, stationary points and max and min points
You forgot a square in the denominator:
=\frac{4x(x^2-1)-2x^2(2x)}{(x^2-1)^2}=\frac{-4x^3-4x-4x^3}{(x^2-1)^2}=\frac{-4x}{(x^2-1)^2})
Which is offcourse don't make any difference in calculating the stationary points, but maybe for the inflection points it does.
