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1-Visitor
May 7, 2011
Solved

Global Maximum/Minimum and tangent

  • May 7, 2011
  • 22 replies
  • 12136 views

Hello together,

hopefully the last question concerning my diplome thesis:

Does Mathcad 15 have a function to find the (Global) Maximum/Minimum of an analytic function, like f(x) = x^3 + x^2 - 4 . I need the x-Value and the y - Value of the Maximum/Minimum.

And additionally, I need to find the tangent from the point of origin to an analytic function, like g(x) = x^2 + 4x -10 . So I need to point at which the tangent touches the given function.

Thanks a lot,

Simon

Best answer by RichardJ

Swap the two sides of the definition.

22 replies

1-Visitor
May 7, 2011

Is there any chance you could upload a worksheet?

You are likely to attract more interest if a worksheet of the problem is included.

Mike

23-Emerald V
May 7, 2011

Simon Kohn wrote:

Hello together,

hopefully the last question concerning my diplome thesis:

Does Mathcad 15 have a function to find the (Global) Maximum/Minimum of an analytic function, like f(x) = x^3 + x^2 - 4 . I need the x-Value and the y - Value of the Maximum/Minimum.

And additionally, I need to find the tangent from the point of origin to an analytic function, like g(x) = x^2 + 4x -10 . So I need to point at which the tangent touches the given function.

Thanks a lot,

Simon

It has symbolic differentiation.

Stuart

19-Tanzanite
May 7, 2011
Does Mathcad 15 have a function to find the (Global) Maximum/Minimum of an analytic function, like f(x) = x^3 + x^2 - 4 . I need the x-Value and the y - Value of the Maximum/Minimum.

You need to be more specific about what you are trying to achieve, Mathcad has functions that will find maxima or minima of functions (including functions of more than one variable) within a given interval. It has a function that will give you all the roots of a polynomial. For many functions you could find the global maxima and minima by using symbolic differentiation. That is not going to work for every function though.

And additionally, I need to find the tangent from the point of origin to an analytic function, like g(x) = x^2 + 4x -10 . So I need to point at which the tangent touches the given function.

There is no built in function to do this, but one could be written. But there may be no such tangent (for example a circle that encloses the origin), there may be more than one such tangent (for example a circle that does not enclose the origin), or there may even be an infinite number of such tangents (e.g the sin function). So, again, you need to be more specific.

24-Ruby IV
May 7, 2011

Simon Kohn wrote:

Does Mathcad 15 have a function to find the (Global) Maximum/Minimum of an analytic function

You can work with user function - with genetic algorithm for example:

http://twtmas.mpei.ac.ru/mas/Worksheets/Minimum.mcd

SimonKohn1-VisitorAuthor
1-Visitor
May 10, 2011

Here is a very simple example. I get the error message that P is not defined. Perhaps someone could post the corrected worksheet.

Thanks a lot

19-Tanzanite
May 10, 2011

A numeric solution using a non-linear solver always requires a guess value.

SimonKohn1-VisitorAuthor
1-Visitor
May 11, 2011

Guys, still having huge problems with more than one variable.

Please see the file.

a) If I use a guess value for x which is not equal to zero, f (x,4) will be wrong.

b) Why the graph for f(x,4) cannot be displayed?

c) Q cannot be determined 😞

12-Amethyst
May 11, 2011

a) Plotting f(x,4) - does not plot because you perviously assigned a value to x; So Mathcad cannot now use x as a range variable for plotting. Change the variable, I used xx in the attached. You could still plot against x, but you must make x vector of values.

b) Minimize(f,x,y) expects variables x and y, not constants. you can change to g(x)=f(x,4) and then Minimize(g,x).

(Richard, that is a nice function, thanks)

SimonKohn1-VisitorAuthor
1-Visitor
May 12, 2011

Thanks Wanye, is there any chance to minimize f(x,4) ? See the file in my posting above.