Find min, max of an unfamiliar function

[truongson243]

Homework Statement

For every x over ℝ, find min, max of following expression

Homework Equations

y=8x⁴/(x²+1)²+4x/(x²+1)+1

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]

Homework Statement

For every x over ℝ, find min, max of following expression

"every x over ℝ" - this shows up as a box in my browser.

Homework Equations

y=8x⁴/(x²+1)²+4x/(x²+1)+1

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?

The Attempt at a Solution

I've graphed it but it's really complex. How can I find that points? Thank you so much :)

 

[Ray Vickson]

Homework Statement

For every x over ℝ, find min, max of following expression

Homework Equations

y=8x⁴/(x²+1)²+4x/(x²+1)+1

The Attempt at a Solution

I've graphed it but it's really complex. How can I find that points? Thank you so much :)

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