@acer 

Thanks

I did something with the Plotbuilder in the worksheet mode
It can be used for code generation too, so for our example with grid [25,25] = 625 points resolution.

Clicking on a plot gives options

ex_set_2_task_7.mw

@acer 
Thanks

Its the right grid area now in your plot , but there no option added for the grid resolution. 

@Carl Love 

Thanks

Yes, i searched in Maple for help and make some progress with the plotbuilder command for worksheet
Now i will try to apply the grid resolution in the implicit plot
The plotbuilder is handy for generating plotcode too.  

Sidenote: Cartesian product,  from René Descartes ( thought has lived here in Amsterdam, there is a house, but open for public? )   

 

@acer  

Thanks

Could nothing find in old study Maple worksheet about double integrals, the area definitions for domain..

But i see also R={(x,y) |  .....} as a set notation for a domain to use in double integrals. 
The rectangle seems to me correct

[ -4,2]x[-4,5] notation example has special handling if you translate to the x-axis and y -axis in 2D and in 3D to  xyz axises and also in Maple syntax too
But this grid area is wherein the implicit curve must be plotted.   

@acer This is an attempt at part ii) using your earlier methodology of Arrays and loops. You may be able to bend it to your task. You certainly don't have to do it this way. (It's not my preference.)

I don't have another choice to do it on a different way and get now a little bit used to see calculations with arrays.

  

@acer 

That grid thing notation rectangle [-4,2] x [-4,5]  can't give meaning to this
The curve must be plotted in this rectangle ? 

Its clear, but 20 years back fsolve was maybe the only solver in Maple ( old shool )
There are some more as you showed in earlier post
I collected them. 
Add this post at the excersises set task post

@acer 

Thanks!

I was doing exc set2 task 7 (i) (ii),(iii)

The first question for 7(i) ..was about to show a portion of the Curve ? 
Do i understand it well that you did 7(ii) and 7 (iii) ?

@Carl Love 

Thanks

A special case if  dividing/multiplying  by zero is not possible. 
I must see this situation

@Carl Love 

Thank

Don't see yet what decision has to be made in the procedure
Has to with the length of the tangentline?

@acer 

Thanks

Looks good for n = 3 and i did  for n = 10 it is becoming rather small the tangentlines, but if the function is periodic then that portion of the plot counts
But perhaps with zooming in the plot i shall better see the tangentlines?
The whole plot for n = 10 shows mainly the blue points without tangentlines -> zoom in 

Its about the variable L what gives room for experimenting
Note: must study closer how this done the deravation for a variable tangentline length
I noticed horizontal tangentline is max length and minimal when the tangent line is almost vertical
Its a visual confirmation about the steepness of the tangentline

This is better than all tangentlines do have a fixed length  ( no comparison needed with another procedure what has fixed lenghts)

Do see a new programing construct : a if with quotes.

@acer 

Thanks

There was no requirement for how long the tangentlines or  inflectionlines should be in the tasks as i can see it now.
Interesting your solution for the tangent length by not taken a fixed length what i proposed.  

I am curious how this will be look in a general procedure for a any number n of tangentlines
Maybe interesting to compare both procedures for their "tangentlengths looks"?      

@acer 

Thanks

There was the idea of make the procedure general voor een given number n of tangentlines, is it not enough to base the tangentlinelength  on a sub-interval length ( some smaller), that should be enough for all tangentline lengths.
Is that not a easier solution ?

@acer 

Thanks

Suppose the slope is 0 of the tangentline then the length must fit, between a sub interval from interval a b -> the tangentpoint lie on the interval point
Maybe can this length be used for all other slopes of the tangentlines 

l@Carl Love 
Thanks
The length of the tangentlines are +- (b-a)/2n  for a given interval 
This can be a plotoption then.

n is number of tangentlines to make it general, but the task was for 6 tangentlines : a interval a b divided in 5 subintervals.

I will try to make it general the procedure for any number of tangentlines
 

@janhardo 

Tried to make as procedure Tangentlines( f,a,b) input : two number a , b as interval, but failed.
Note : in Holland we are used to one Capital letter for words : example: Raaklijnen is (TangentLines)
 

I succeeded in adding the x-valus for the tangentpoints and adding a legenda in the procedure.

betounes_ex_set_2_opg_6via_codeexample2.3_uitwerking_ac.mw

@Carl Love 

Thanks

Good to point this out and keep in mind