## 375 Reputation

10 years, 91 days

## @acer  As you wrote : @janhardo&n...

As you wrote :

@janhardo No, it's not a lot more work. Look, the same approach can be done as in the earlier attachment you gave, CD2-5.MWS. The loops are merged together, as I mentioned could be done.

Is there a benefit to make from one array do loop a two nested do loop ?

G := Array(1..6, 1..3):
P := Array(1..6):
for i from 1 to 6 do
G[i, 1] := L[i];
G[i, 2] := df(G[i, 1]);
G[i, 3] := f(G[i,1])+G[i, 2]*(x-G[i,1]);
P[i] := plot(G[i,3], x=G[i,1]-1..G[i,1]+1, colour=red);
end do:

-----------------------------------------------

This one does do  the same

B := Array(1..6,1..3):
for i from 1 to 6 do
for j from 1 to 3 do
B[i, 1] := L[i];
B[i, 2] := df(G[i, 1]);
B[i, 3] := f(G[i,1])+G[i, 2]*(x-G[i,1]);
end do;
end do:

## @acer Thanks!Now i do see something...

Thanks!

Now i do see something similar code as in the book, thought first that absence of a regularity in the x-values of f was the problem, but now using a list for random x

It is better for developing programming skill to use those loops?

"The loops are merged together, as I mentioned could be done."   .... i must look at this ?..ah yes that was the earlier answered task by you  to use a nested do loop for a two-dimensional array

That i think also the intention of the task to use nested do loops , but i can be also be done with a a single loop, if i am i correct.

## @acer Is it not possible to use a 6...

Is it not possible to use a 6x2 array for storing the inflection points and y'

The inflection points  for function f are called by: (calculated earlier by you )
Q := map(p->[p,f(p)], Inflpts);

Question :  those  < >  ?

G[1..6, 1] := <Student:-Calculus1:-Roots(ddf(x), x=0..16, numeric)>;

----------------------------------------------------------

Note : The length of the tangentlines must be on a interval  ( see task ) :

## @acer ThanksThere is a lot to study...

Thanks

Interesting you have worked out the task now with array..could try this approach in my task

It is a lot of work you did opposite the bookexample code
But in the bookexample it is drawing tangentlines randomly chosen at  x= 0.5,.1.5,2.5,..,5.5 (regularity)  and x=0.5+(i-1) to fill

with a loop the x-values in a array.

In the task ex set 2-task 3 there are x -values without regularity , so no general formulae to find for using in a do loop

I learned a lot now.

There is a lot to study for this introduction programming...MCtoc.mws

## @tomleslie ThanksI thought in Engli...

Thanks

Now  you drawed the tangentlines in the 6 infliction points of  the graph by a procedure.

Not all is clear for me in the procedure how set this up by you, but that's way i try to learnn programming from the book.

I thought in English language that inflection points also included mins and maxs of a function

That's way i started with a first derative of the function

Next time i give a screenshot of the question of the task , so there will be no room for errors

## @acer ThanksIts all about using in ...

Thanks

Its all about using in the :  exercise set 2-task 3..  array's and how to come up with them (invent) and to get used of them
In the book the use is widespread

Your approach of the task 3 is a different one then is  done in book.
That is the problem here: i don't have the answers from the author in Maple from the book and try to follow the book    CD2-5.MWS

Note: in enclosed worksheet the tangentlines in maxs or mins of function are not 0 (horizontal) in the  plot :  y' = 0 , strnge that this is not done in the example  -> no it was done for a serie of x-values ( not for x where f '=0 ), so its correct the positions of the tangentline

## @acer I am following the book where...

I am following the book where are array used  and not vector or matrix ( it s not vector calculus or matrix calculus what's written in book at the moment )

The array is used to store different type of data (types) in Maple : set of points, a equation, a plot  like that.
The next time i upload a worksheet with array questions

## @janhardo  It is difficult to fill...

It is difficult to fill the arrays with the right content ..the reasoning

 >

 >

Inflction point : buigpunt

 Tangent Lines (Examples 2.1 and 2.3)
 > restart;
 > with(Student:-Calculus1): with(plots):
 > f:=x->x^sin(x);intvx:= x =0.1..16;
 (1)
 > plot(f(x), intvx, gridlines= false);
 > C:=plot(f(x), intvx, gridlines= false):
 >

i see 6 inflection points in the graph

 > df:=D(f);
 (2)
 > df_expr:=x^sin(x)*(cos(x)*ln(x)+sin(x)/x);
 (3)

Uitzoeken van functievoorschrift naar expressie ivm solve argument-(niet meer nodig ?)

 >
 > X:= solve( df_expr =0, x); # standaard solve is niet werkend
 (4)

This is not working this solve for  fprime , so i asked on Mapleprimes forum : needed with(Student:-Calculus1):

 > Roots(df(x), x=0.1..16, numeric);
 (5)
 > # Second derivative ddf := D(D(f));
 (6)
 >

==============================================================================

 > Roots(ddf(x), x=0.1..16, numeric);
 (7)
 > InflectionPoints(f(x), x=0.1..16, numeric);
 (8)
 > Inflpts := [ fsolve(ddf(x), x=0..16, maxsols=6) ];
 (9)
 >

=======================================================================

 >

Roots / InflectionPoints / Inflpts  give the same answer.
Now in the spirit of Tangentline example  drawing the tangentlines int he infliction points

The idea is to use two arrays : G and  P for storing inflection points, equation of tangentline and plot tangentline in function f.
The dimension for array G (matrix) is : 6 infliction points = 12 cells  and  6 cells for equation tangentline
Dimension array G:. 6 points + equation tangentline   ( 6 rows and 3 colums ) : every row can store 3 datatypes.

-The inflection points  and the equation of the tangent lines to the graph of f

are to be stored in a 6 by 3 array called G.

-The plot of f and  the plots of the tangent lines are to be stored in an array P.  First, we declare these arrays.

The first row of array G stores the x-value of the first point, the y-value of the first point,  and the equation of the tangent line at the first point.  The second row of G will contain the same information for the second point, the third row the information for the third point, and so on.  The element P[1] of array P will contain the plot of the tangent line at the first point, P[2] will contain the plot of the tangent line at the second point, and so on.  All these assignments can be made easily with the following do loop.

 > for i from 1 to 6 do      G[i,1]:= 0.5+(i-1);      G[i,2]:= f(G[i,1]);      G[i,3]:= G[i,2]+fprime(G[i,1])*(x-G[i,1]);      P[i]:=plot(G[i,3],x=G[i,1]-0.8..G[i,1]+0.8,thickness=2):  od:

You must have asked yourself the question with a given function f  : what do i need for plotting the tangentlines in the inflectionpoints  of graph f ?
Looking at the for statement  ...

 > G:=array(1..6,1..3): # definition of 6 rows and 3 colums array
 > P:=array(0..6):

The inflection points  for function f are called by:

 > Q := map(p->[p,f(p)], Inflpts);
 (10)
 >

To define the equations of the tangent lines we need their slopes.  Thus, we need the derivative function of f.

 > df:=D(f);
 (11)
 >

## @acer ThanksIts primarily for Maple...

Thanks

Its primarily for Maple programming and doing recreational math.
Basic calculus i know something : function of two variables , double integrals and some more

But i am a B ed in math focussed on teaching a not a bachelor or master in math who do have stronger math knowledge/skills

Indeed i gave y' at the start of the thread, because i thought that inflection points also were mins and maxs y-values in the english language for y

## @janhardo  For finding real roots ...

For finding real roots there was also another command used: it can be added to the list

RootFinding:-Analytic(diff(fprime_expr,x,x)=0, re=0..10, im=-1..1);

## ThanksNice workAh i do see the use now o...

Thanks

Nice work

Ah i do see the use now of the fsolve command:

The enclosed example uses array, because they are versatile for programming to use as it seems

The bookexample draws a tangentline on mins and maxs of y, while this task is for the infliction points of y

Thanks

## @acer   ......

 >

I thought i could do the task step by step (learning step by step)

The calculations made on reaction on question are very useful for me to see basis calculus with plots to learn more

Here is the task where i am working on , could be interesting to see if there are more answer are possible opposite  the direction of the book is aiming for.

But that is a lot work and that's why i tried to do it step by step and come up with a own solution

CD2-5.aangepast.mwsCD2-5.aangepast.mws

Thanks

Impressive..

The task is draw in y the tangentlines in all 6 inflection points of y on  interval  0.1..16  ( so the y '' is needed)
So inspection by sight shows then 6 infllection points for ( your calculation use 0..10 )

Yes, change sign must then be shown in  y '' to conclude were y  has inflectionpoints with a particular direction.

https://www.hhofstede.nl/modules/buigpunten.htm

## @tomleslie  Thanks  I could c...

@tomleslie
Thanks

I could chance in the procedure the functions : it is y and y ' , so the y plot with the inflection point depicted then

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