1. The problem statement, all variables and given/known data For every x over ℝ, find min, max of following expression 2. Relevant equations y=8x^{4}/(x^{2}+1)^{2}+4x/(x^{2}+1)+1 3. The attempt at a solution I've graphed it but it's really complex. How can I find that points? Thank you so much :)
"every x over ℝ" - this shows up as a box in my browser. I'm assuming that you wrote the right side correctly, where there are three terms, with 1 being a term by itself. Rewrite the right side as a single rational expression. What is the least common denominator?
You need to use Calculus, setting the derivative to zero. That gives you a 4th degree polynomial to solve; its two real roots correspond to the max and min. (They are the roots of the polynomial x^{4} - 8x^{3} - 1.) RGV