Find the maximum of a function - HP 50G - HP Support Community

juanjuan · ‎08-06-2015

Hello everyone. I have to find the maximum of a function. I know how to do it without the calculator but it takes me a lot of minutes, so I need to know if I can do it with the HP 50G easier.

The function is:

f(x)= - 6/((x^4)*ln(x)) - 11/((x^4)*ln^2(x)) - 12/((x^4)*ln^3(x)) - 6/((x^4)*ln^4(x))

I need to find:

max |f(x)|

with e<x<e+1

The answer is:

max |f(x)| = 0.64105

Thanks!

andy11 · ‎08-06-2015

I'm afraid there is no single function which finds extrema of a function.

So one of possibilities would be find a derivative of your function (u can use DERIV) and then find zeros of the derivative (with ZEROS). Details of use of DERIV and ZEROS you can find in the refrrence manual. As you can solve this problem manually you must be fluent in math, so this general remark should be sufficent for you. Or maybe someone else knows a better solution.

Maké · ‎08-07-2015

Hi!, juanjuan:

Try, with absolute value, with ...

<< -> X '-(6/(X^4)*LN(X)))-11/(X^4*LN(X)^2)-12/(X^4*LN(X)^3)-6/(X^4*LN(X)^4)' ABS >>

Store with any name, the local variable

If you configure FLAG

03 Function -> num

Number Format .... Fix 11

When you put, ... e (RPN Operating Mode) and press ENTER key, appear ... 2.71828182846

Now press the key Function (F1...F6), where have the name of local variable.

Then ... .641047361105

And for e 1 + (RPN Operating Mode), appear 3.71828182846 and after, you must see ... .095539588610

Kind Regards !.
Have a nice day !.
@Maké (Technical Advisor Premium - HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/

Maké · ‎08-08-2015

Hi!, juanjuan:

You can see, too ...

http://h30434.www3.hp.com/t5/Other-HP-Consumer-Products-and-Technologies/HP-Prime-calculating-bug/td...

http://www-fourier.ujf-grenoble.fr/~parisse/giac/doc/en/cascmd_en/node61.html

Kind Regards !.
Have a nice day !.
@Maké (Technical Advisor Premium - HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/

calcpeace · ‎08-10-2015

Hello all,

I think here it is a little bit tricky, because the function |f(x)| has in the aera for x ( ] e ; e+1[ ) no relative maximum, only a maximum on the left border (for e). So the simple method first deriviate is zero fails.

But the hp 50g don't plot the funktion |f(x)| in the right way, it seems that the machine ignores the absolute value function.

andy11 · ‎08-11-2015

Absolut value of the function given by juan in the 1st mail is plotted just right on my 50g. Could you give an example of a function which abs val is plotted in a wrong way?

calcpeace · ‎08-11-2015

Hello Andy11,

I checked some pages in the web to find what's going wrong. If you clear flag 119 (= rigorous on) the graph is plotted correct. There is no plotting problem any longer.

greetings

calcpeace

Maké · ‎08-11-2015

Hi!, calcpeace or peacecalc:

The draw is correct, but the error, is same "Bad guesses".

Kind Regards !.
Have a nice day !.
@Maké (Technical Advisor Premium - HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/

Maké · ‎08-11-2015

Hi!, juanjuan:

You can comparise with Wolfram Mathematics ...

Kind Regards !.
Have a nice day !.
@Maké (Technical Advisor Premium - HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/

Maké · ‎08-11-2015

Hi!, juanjuan:

You can comparise, with Wolfram Mathematics ...

Input:

$f(x) = -6\/(x^4 log(x))-11\/(x^4 log^2(x))-12\/(x^4 log^3(x))-6\/(x^4 log^4(x))$

Plots:

Complex-valued plot

Real-valued plot

Complex-valued plot

Real-valued plot

Alternate forms:

$f(x) = -(log(x) (log(x) (6 log(x)+11)+12)+6)\/(x^4 log^4(x))$

$f(x) = -(6 log^3(x)+11 log^2(x)+12 log(x)+6)\/(x^4 log^4(x))$

Alternate form assuming x is positive:

$x^4 f(x) log^3(x)+6 log^2(x)+11 log(x)+6\/(log(x))+12 = 0$

Properties as a real function:

Domain:

Range:

Surjectivity:

Derivative:

$d\/dx(-6\/(x^4 log^4(x))-12\/(x^4 log^3(x))-11\/(x^4 log^2(x))-6\/(x^4 log(x))) = (24 log^4(x)+50 log^3(x)+70 log^2(x)+60 log(x)+24)\/(x^5 log^5(x))$

Indefinite integral assuming all variables are real:

$integral (-6\/(x^4 log(x))-11\/(x^4 log^2(x))-12\/(x^4 log^3(x))-6\/(x^4 log^4(x))) dx = 2\/(x^3 log^3(x))+3\/(x^3 log^2(x))+2\/(x^3 log(x))$

Indefinite integral assuming all variables are real:

$integral (-6\/(x^4 log(x))-11\/(x^4 log^2(x))-12\/(x^4 log^3(x))-6\/(x^4 log^4(x))) dx = 2\/(x^3 log^3(x))+3\/(x^3 log^2(x))+2\/(x^3 log(x))+constant$

Kind Regards !.
Have a nice day !.
@Maké (Technical Advisor Premium - HP Program Top Contributor).
Provost in HP Spanish Public Forum ... https://h30467.www3.hp.com/

Find the maximum of a function - HP 50G

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