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**3d_guru****Member**- Registered: 2006-01-02
- Posts: 5

again..i've uploaded the picture because it's easier to write it in Mathematica..

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

If you use Mathematica it's easy.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Put the following code:

```
Print["The Function:"]
f[x_]:=((x^2)Log[x])/ \[ExponentialE]
f[x]
Print["The Derivate:"]
f'[x]
Print["The roots:"]
Solve[f'[x] == 0, x]
```

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

And you can include Plots:

```
Plot[f[x], {x, 0, 10}, AxesLabel -> {x, f[x]}]
Plot[f[x], {x, 0, 1}, AxesLabel -> {x, f[x]}]
Plot[f'[x], {x, 0, 10}, AxesLabel -> {x, f'[x]}]
Plot[f'[x], {x, 0, 1}, AxesLabel -> {x, f'[x]}]
```

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Here is the program:

(demonstrates the power of Mathematica once again)

*Last edited by krassi_holmz (2006-01-06 01:41:21)*

IPBLE: Increasing Performance By Lowering Expectations.

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**3d_guru****Member**- Registered: 2006-01-02
- Posts: 5

hey thanx krassi_holmz..didn't know Mathematica was so powerfull.

oh man and the code is so simple, that's great!

thanx again..i appreciate it

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Haven't you read Mathematica help?

It's hundred times powerful than this. It's just a simple example.

*Last edited by krassi_holmz (2006-01-06 02:15:32)*

IPBLE: Increasing Performance By Lowering Expectations.

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**God****Member**- Registered: 2005-08-25
- Posts: 59

Derivative =0

x^2 = 0, x = 0

or

2xlnxe - lnx = 0

lnx(2xe-1) = 0

lnx = 0 or 2ex - 1 - 0

x = 1 or x = 1/(2e)

So, horizontal tangents occur at

x = 1

x = 1/(2e)

x = 0

Double check that the second derivative is never equal to 0 for each of those points... when it does, it isn't an extrema

*Last edited by God (2006-01-08 09:21:56)*

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