In my work developing Maplets for Calculus, there are many instances when I want to determine that a function is monotone (decreasing or increasing or non-decreasing or non-increasing) on an interval. If I can do one of these, I can do them all. So, let's focus on decreasing. I have no problem assuming f is continuous and differentiable on the interval. The interval could be unbounded, and I am not terribly concerned about endpoints (at least now). Given a function f, how would you use Maple to determine that f is decreasing on an interval (possibly unbounded)?

Origami and thales theorem See this.

As a math phobic, I took a class this semester at UConn Math102Q. The instructor is pretty good but now at mid-semester there are a lot of "do more problems" answers. I hoped at the beginning this would help with my math phobia. The course is fairly new and uses the PSSSP model and the book is written by DeFranco and Vinsonhaler.

We are pleased to announce the first winners of the monthly Maple Mentors Awards. Jacques Carette and Robert Israel will receive a prize of their choice to thank them for their involvement with the MaplePrimes community. Jacques has consistently been a valuable member of MaplePrimes, posting clear and insightful information on advanced topics. Robert in particular has been active in the Student Forums on MaplePrimes since their inception and we would like to recognize this. One member had these comments on the two:

As new features are being built into upcoming releases of Maple, here is one request that would be very helpful for those of us who use Maple to teach lower-level (Calculus) students. Maple can work nicely with functions, but students are not always so comfortable with this language. Here's a current example. Suppose you want to find the tangent line to a function. We might work as follows.

> f := x -> sqrt(4-x^2);
                                      /     2\
                             x -> sqrt\4 - x /
> df := D( f );           # typed, or from context-menu
                                         x      
                            x -> - ------------
                                       /     2\
                                   sqrt\4 - x /
> TL := f(1)+df(1)*(x-1); # tangent line at (1,sqrt(3))
                           (1/2)   1  (1/2)        
                          3      - - 3      (x - 1)
                                   3               

This works nicely and looks fine. Now change the function.

f := x -> sin(x);
                                 x -> sin(x)
df := D( f );           # typed, or from context-menu
                                     cos
TL := f(1)+df(1)*(x-1); # tangent line at (1,sin(1))
                           sin(1) + cos(1) (x - 1)

This works fine, but does not LOOK good. The problem is that Maple is TOO SMART. It knows that the derivative function (x->cos(x)) is simply the cosine FUNCTION. Instead of the abbreviation (cos) I want to be able to tell Maple to show this result as (x->cos(x)).

Find the equation to a line that contains the point (-4, -3) and is perpendicular to the line x^2+y^2=25.

I recently posted to the Applications Center a set of class notes and a solutions manual for the exercises to accomany a course in Multivariable Calculus. These notes are a result of teaching this course for the last number of years to Engineering students at NSAC and they have found them to be benificial. I am interested in any comments and/or suggestions on how they could be improved for later editions. Link to Application on Maplesoft App Center

In the following working Maple 11 worksheet an error ("Error, (in rtable/Product) invalid arguments") occurs if "array" is changed to "matrix". Also, if I change "Vector" to "array" I don't get the answer that I want. I get the same error if I use the Matrix Palette to define the matrix. View 4937_SE.mw on MapleNet or Download 4937_SE.mw
View file details Please help me understand these things better.

Does anyone know how to solve this equation 49x + 24y + 37z = 3778171

hi..im a student from malaysia..

It's a new day, but not a new problem. Yesterday I asked about solving inequalities with abs. Today I am looking at solving an equation with abs. Try the following:

restart;
q :=  sin(x)/x - 1:
test4 := y -> [ y,
                solve( q=y, x ),
                [solve( abs(q)=y, x )],
                fsolve( q=y, x ),
                fsolve( abs(q)=y, x ) ]:
test4(  0  );
test4( 0.1 );
test4( 0.5 );
test4( 1/2 );
test4(  1  );

[                         /sin(x)           \                -13]
[ 0,   0, [0],      fsolve|------ - 1 = 0, x|, 1.869896012 10   ]
[                         \  x              /                   ]

Quick, what numbers x satisfy:

abs( x-2 ) < 1

How does Maple answer this?

solve( abs( x-2 ) < 1, x );
                         RealRange(Open(0), Open(2))

Now, change the RHS to 1. (floating-point 1):

solve( abs(x-1) < 1., x );
           RealRange(1., Open(2.)), RealRange(Open(0.), Open(1.))

Of course, these two intervals can be combined to the one interval. Maple 10 did not have this problem. (I will explain what Maple 11 is doing later, I want the next paragraph to appear in the truncated version of this post.) This issue is important for those of us trying to use Maple in the classroom. While it's not difficult to explain what is going on, the point is that this is not the mathematics I am trying to teach and these issues are a distraction.

I need help with a problem. There are 24 square tables, but the tables must be formed as rectangles. i.e. two together. How many combinations can be made with the 24 tables. What is the maximim number of people to sit at the tables using what combination What is the least number of people to sit at the tables using what combination.

The latest edition of TUGboat (vol. 28 no. 2, 2007), the journal of the TeX users group, contains an article by Edward Reingold, Writing numbers in words in TeX, which, as its title states, gives TeX macros for converting integers to names. In this case, American English names. For my amusement Sunday I wrote the equivalent procedure in Maple.

Hi How do I find the max possible volume of the following cylinder when volume given as V=pi(6r^2 -r^3). The sum of its radius and height is 6cm.