# Help with graph please- concavity, relative extrema, etc.

• Feb 6th 2010, 08:40 AM
BigMath
Help with graph please- concavity, relative extrema, etc.
2x^2+1
--------
2x^2-3x

Show any asymptotes, relative extrema, inflection points, concavity, and where the function is increasing or decreasing.

I'm really having trouble with this (Headbang), any help would be GREATLY appreciated.

Thanks guy/girls.
(Rofl)
• Feb 6th 2010, 09:01 AM
VonNemo19
Quote:

Originally Posted by BigMath
2x^2+1
--------
2x^2-3x

Show any asymptotes, relative extrema, inflection points, concavity, and where the function is increasing or decreasing.

I'm really having trouble with this (Headbang), any help would be GREATLY appreciated.

Thanks guy/girls.
(Rofl)

Set $f'(x)=0$ to locate any extrema.

If $f'(x)$ is undefined at some number $x=c$, then $x=c$ is a vertical asymptote.

If $\lim_{x\to\pm\infty}f(x)=L$, then $f(x)=L$ is a horizontal asymptote.

Get started with that and then show me what you've got.
• Feb 6th 2010, 09:05 AM
BigMath
That's basically all I know how to do:

For H.A. I got: 1

For V.A. I got: 3/2, 0

For the increasing/decreasing do i solve for first derivative than make it equal 0? Or do I use the V.A. points and plug in to the first derivative.
• Feb 6th 2010, 09:11 AM
VonNemo19
Quote:

Originally Posted by BigMath

For the increasing/decreasing do i solve for first derivative than make it equal 0?

$f'(x)>0$ means that $f$ is increasing.

$f'(x)<0$ means that $f$ is decreasing.

So, you must solve these inequalities to determine the invervals over which $f$ is increasing or decreasing.
• Feb 6th 2010, 09:18 AM
BigMath
My teacher wanted us to make a chart, with infinity to certain number, certain number to another, and that number to negative infinity and to plug in numbers to get increasing/decreasing. Can you show me?
• Feb 6th 2010, 09:19 AM
VonNemo19
Quote:

Originally Posted by BigMath
That's basically all I know how to do:

For H.A. I got: 1 correct

For V.A. I got: 3/2, 0 correct

For the increasing/decreasing do i solve for first derivative than make it equal 0? Or do I use the V.A. points and plug in to the first derivative.

.
• Feb 6th 2010, 09:25 AM
BigMath
For the numbers you plug in the first derivative, to see if they are greater or less than 0, where do you get those numbers from? Do you use the V.A.?
• Feb 6th 2010, 09:28 AM
BigMath
Are they

-infinity, -1.115

-1.115, 0.448

0.448, 0

0, 3/2

3/2, infinity

Than plug in numbers in between to see increasing or decreasing?
• Feb 6th 2010, 09:41 AM
VonNemo19
Quote:

Originally Posted by BigMath
My teacher wanted us to make a chart, with infinity to certain number, certain number to another, and that number to negative infinity and to plug in numbers to get increasing/decreasing. Can you show me?

I'm not skilled enough with LaTeX to make a chart on this forum, but the idea is to choose test values between the critical numbers to see if $f'>0$ or $f'<0$.

$f(x)=\frac{2x^2+1}{2x^3-3x}$

$f'(x)=\frac{(2x^2-3x)(4x)-(2x^2+1)(6x^2-3)}{(2x^3-3x)^2}$

$=\frac{(8x^3-12x^2)-(12x^4-3)}{(2x^3-3x)^2}$

$=\frac{(8x^3-12x^2)-(12x^4-3)}{(2x^3-3x)^2}=0$ implies

$(8x^3-12x^2)-(12x^4-3)=0$

$8x^3-12x^2-12x^4+3=0$

$12x^4-8x^3+12x^2-3=0$ Which is really ugly. Are you sure that this is the right problem?
• Feb 6th 2010, 09:46 AM
BigMath
http://www.mathhelpforum.com/math-he...e0ff24fe-1.gif

The bottom is 2x^2-3x

Derivative comes out to like:

-6x^2-4x+3
----------
(2x^2-3x)^2

No idea why that is underlined

So when I solve for 0, I get

-6x^2-4x+3=0

I used the quadratic formula.

• Feb 6th 2010, 09:54 AM
VonNemo19
Quote:

Originally Posted by BigMath
http://www.mathhelpforum.com/math-he...e0ff24fe-1.gif

The bottom is 2x^2-3x

Derivative comes out to like:

-6x^2-4x+3
----------
(2x^2-3x)^2

No idea why that is underlined

So when I solve for 0, I get

-6x^2-4x+3=0

I used the quadratic formula.

ooops. My bad. OK, yeah, so it doesn't factor. Using the quadratic formula should give the two answers that you've given before.

Yeah. You're on the right track. So, make a table that describes the sign of f prime at some test value on the intervals that you have already discovered a couple of posts ago before I went in left field with doing the wrong problem.
• Feb 6th 2010, 09:59 AM
BigMath
Okay I got this:

Than I plug it into the first derivative to see increasing or decreasing:

f1(x) f(x)
-infinity, -1.115 - dec

-1.115, 0.448 + inc

0.448, 0 + inc

0, 3/2 - dec

3/2, infinity - dec

Are those the right points I would use? So can you help me check this so far:

Increasing/decreasing: see above

Relative max: (0, f(0))

Relative min: (-1.115, f(-1.115))

Right or wrong?