any examples to show d2y/dx2 of max/min point can be 0

• September 10th 2010, 01:49 AM
stupidguy
any examples to show d2y/dx2 of max/min point can be 0
Any good examples showing ${d2y}/{dx2}$of max/min point can be 0?

Thanks.
• September 10th 2010, 02:03 AM
sa-ri-ga-ma
y = ax +b

Try this one.
• September 10th 2010, 02:28 AM
stupidguy
Quote:

Originally Posted by sa-ri-ga-ma
y = ax +b

Try this one.

the qn is max or min point, not straight line.
• September 10th 2010, 03:37 AM
mr fantastic
Quote:

Originally Posted by stupidguy
Any good examples showing ${d2y}/{dx2}$of max/min point can be 0?

Thanks.

y = x^(2n) where n > 1.
• September 10th 2010, 03:43 AM
stupidguy
Quote:

Originally Posted by mr fantastic
y = x^(2n) where n > 1.

Can I show the 3 graphs in LATEX?
• September 10th 2010, 11:24 AM
Soroban
Hello, stupidguy!

Quote:

$\text{Any good examples showing }\frac{d^2y}{dx^2}\text{ of max/min point can be 0?}$

mr fantstic nailed it!

$y \:=\:x^4$ is shaped like a parabola, but rises more steeply
. . and is "fatter" near the origin.

Code:

              |   *          |          *               |               |   *          |          *               |     *        |        *     *        |        *       *      |      *           *  |  * - - - - - - - * - - - - - - -               |

There is a minimum at (0,0).

The concavity is 0 because the curve "flattens" slightly there.

• September 10th 2010, 11:48 AM
ebaines
Here's another:
$
y = \frac x 2 - \frac {sin 2 x} 4
$

You get
$
y' = sin^2 x
$

$
y'' = 2 sinx\ cosx
$

Attachment 18879
• September 10th 2010, 11:57 AM
stupidguy
how did you plot a graph? did you use latex?
• September 10th 2010, 12:18 PM
ebaines
Quote:

Originally Posted by stupidguy
how did you plot a graph? did you use latex?

Maybe there's an easier way, but what I do is make the graph in Excel, then take a screen shot of the graph, save it as a jpg, then use the Attachments tool under "Go Advanced."
• September 10th 2010, 12:25 PM
stupidguy
Quote:

Originally Posted by ebaines
Maybe there's an easier way, but what I do is make the graph in Excel, then take a screen shot of the graph, save it as a jpg, then use the AtTtachments tool under "Go Advanced.

I am so touched that you did so much to explain to me without any return.(Crying)(Clapping)(Kiss)