@Carl Love 

Thank you. your comand shows that for example both Pi/4 and 9Pi/4 are exactly similar. But we know 9Pi/4 has one circle more than Pi/4. How can we show this case in maple output?

@Carl Love 

Dear Dr Devore,

I am a PhD candidate of Mathematics Education at Ferdowsi University of Mashhad, Iran.

As part of my study, I have permitted by Ministry of Science, Research, and Technology to visit a foreign

university related to my PhD study for a period of six months.

I am very enthusiastic about your research about Maple.

Therefore, I am writing to discuss the possibility of visiting your university and working in your supervision.

In my PhD study, I am investigating freshman students' understanding in learning derivative concept with Maple for creation multiple representations and develop mental constructions based on APOS Theory (Dubinsky, 1983).

 The main objectives of this study are searching how and why using Maple in Teaching Calculus by focusing on derivative.  The current study tries to address the whether process of use Maple in teaching Derivative will develop mental constructions of students in learning Calculus. 

If you have any questions, please do not hesitate to contact me. I truly appreciate your feedback.

Yours Sincerely.

Vahid Borji

PhD student in Mathematics Education

Ferdowsi University of Mashhad, Iran

@marc sancandi 

Thank you for your response.

But It is not what I need.

I need a procedure in Maple 18 that it receives:

Inputs: function f(x) and real unmbers a and b (as interval [a,b]) and natural unmber n 

then devides interval [a,b] to n subinterval and computes f'(a), f'(a+(b-a)/n), f'(a+2(b-a)/n),..., and f'(a+n(b-a)/n)=f'(b)

and

showes at output: graph f(x) and all points [a,f'(a)], [a+(b-a)/n, f'(a+(b-a)/n)],[a+2(b-a)/n, f'(a+2(b-a)/n)]..., and [a+n(b-a)/n,f'(a+n(b-a)/n)] on a coordinate plane x-y

with(plots);
D2 := proc (f, a)

local m, x, y, p1, p2;

m := limit((f(x)-f(a))/(x-a), x = a);

y := m*(x-a)+f(a);

p1 := plot({f(x), y}, x = a-3 .. a+3);

p2 := pointplot([a, m], symbol = circle, symbolsize = 15);

display(p1, p2)

end proc;
f := proc (x) options operator, arrow; x^3 end proc;

@Carl Love 

This is a teaching approach for sketch f'(x) with many plots of (x, f '(x)). I use this approach to promot students' understanding for sketching graph f'(x) by plots (x, f'(x)) such as (a, f'(a)) , (b, f'(b)) and (c,f'(c)) and etc. If you can write such a code that include curves f(x), y=m*(x-a)+f(a) and also the point (a,f'(a)) please submit in here.

@rlopez 

Thank you for your response.

But the task template doesn't show the point (a,f'(a)) and however I need a code with procedures in Maple. If you can write such a code that include curves f(x), y=m*(x-a)+f(a) and also the point (a,f'(a)) please submit in here. (how write such a procedure is very important for me)

@Carl Love 

Thank you for your response. Unfortunately, after use of your commands I see this error:

Error, (in Student:-VectorCalculus:-*) invalid terms in product: (t = -6*Pi .. 6*Pi)*(thickness = 3)
How I can correct this error?

@tomleslie 

Thank you for your response. Unfortunately, after use of your commands I see this error:

Error, (in Student:-VectorCalculus:-*) invalid terms in product: (t = -6*Pi .. 6*Pi)*(thickness = 3)
How I can correct this error?

@rlopez

Thank you for your response.

Yes, It is true and better with diff, too.

But I want to write a proc for Mean Value Theorem by myself. How can I add a condition for a local variable? For example how cn I add a condition to c varibale that c be betwen a and b in my proc?(a<c<b)

@Carl Love 

I use command plot(sin(x)/(tan(x)+x),x=-1..1,discont=[showremovable]); and command plot((x^2-1)/(x-1),x,discont=[showremovable]). but in first case x=0 is not a hollow point and in second case x=1 is a hollow point. why in the first case appears automatic simplification and in the second case doesn't appear automatic simplification?