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truongson243 Feb26-12 03:22 PM

Find min, max of an unfamiliar function
 
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 Feb26-12 05:28 PM

Re: Find min, max of an unfamiliar function
 
Quote:

Quote by truongson243 (Post 3785716)
1. The problem statement, all variables and given/known data

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

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

Quote by truongson243 (Post 3785716)

2. Relevant 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?
Quote:

Quote by truongson243 (Post 3785716)


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 :)


Ray Vickson Feb26-12 07:28 PM

Re: Find min, max of an unfamiliar function
 
Quote:

Quote by truongson243 (Post 3785716)
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 :)

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


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