@acer 

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 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 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 

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 

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 

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 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 the arrays with the right content ..the reasoning
 

Download betounes_ex_set2_task_3.mw

@acer 

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 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);

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

Peter Stone i knew already

@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 

Download betounes_ex_set2_task_3_vraagforum.mw

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

@acer 

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