Find min, max of an unfamiliar function

truongson243

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=8x⁴/(x²+1)²+4x/(x²+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 :)

Mark44

"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?

Ray Vickson

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 x⁴ - 8x³ - 1.)

RGV