I have a curve C with the equation $$y =\frac{4x^2-3x}{x^2+1}.$$
From the previous section of the question, I have written the equation of C in the form $$y =-\frac{1}{2}+\frac{(3x-1)^2}{2(x^2+1)}$$ and $$y=\frac{9}{2} - \frac{(x+3)^2}{2(x^2+1)}.$$
Then, I am required to state the coordinates of the turning points of C without differentiating, which I am stuck. Please help.
The first equation shows that $y\ge -\frac{1}{2}$ for all x, with $y=-\frac{1}{2}$ when $x=\frac{1}{3}$,
and the second equation shows that $y\le\frac{9}{2}$ for all x, with $y=\frac{9}{2}$ when $x=-3$.