For completeness, I sent this to support and they were unable to reproduce the problem so I have no clue what is causing it. At least I know it is not isolated to my computer from the post above by Roman. They did indicate that they would be dropping support for 10.3.9. Unfortunately, I am not in a position to upgrade my hardware right now and it does not meet the minimum requirements for 10.5. My EMP membership was due for renewal as of today but I decided to let it go since I have no idea when the next release is or if it will fix the problem. On the upside, Mathematica 6 is working just fine so it looks like its MathGroup from now on. It was fun while it lasted.

Best,

Thomas

By any chance do any of you have Maple running on PPC OSX v10.4? I am wondering if it could be related to 10.3.

I am not sure which apps use Java or how to tell if they do. The only other apps that I noticed a similar problem with are the chess program that came installed and a typing program (Ten Thumbs) I downloaded a long time ago. These two programs were actually much worse, when I start to use them the CPU bar goes straight to the top and will sit there, even if I do nothing, until I quit the program. Is there a way I can tell what programs are using Java to know for sure? I don't get this behavior with Mma and I think it also has a Java interface, but I am not sure.
edit: OSX version 10.3.9

Note that I did not just replace {} with [], but also change the order in the list (p2 and p3 are now at the end). Did you also change the order?

Note that I did not just replace {} with [], but also change the order in the list (p2 and p3 are now at the end). Did you also change the order?

Let q = the number of quarters and d = the number of dimes. Then you have enough information to make
two equations in two unknowns.
q + d = 8 and 0.25q + 0.1d = 1.25
Since d and q must be positive integers we can use isolve (see ?isolve in the help)
restart:
eq1:= q + d = 8;
q + d = 8
eq2:= 25*q + 10*d = 125;
25 q + 10 d = 125
isolve({eq1, eq2});
{q = 3, d = 5}
Note: I had to write the second equation without decimals to get isolve to work.

ok so this is similar to the example that Robert gave. Look at the graph
restart:
f:= -x^4+11*x^3-38*x^2+52*x-14;
plot(f, x=-2..7, y=-60..60);
In this case you have a pretty good idea that there are only going to be two points (x1, f(x1)) and (x2, f(x2)) that have a common tangent line. But in order to find a and b for the equation of the tangent line, you need to know what two points have a common tangent line. That is you need to know (x1, f(x1)) and (x2, f(x2)) where the common tangent line touches the graph. To find these two points you need to know x1 and x2. You are not just finding a and b, you have to find a, b, x1, and x2. So you need four equations in this case as Robert indicated.

ok so this is similar to the example that Robert gave. Look at the graph
restart:
f:= -x^4+11*x^3-38*x^2+52*x-14;
plot(f, x=-2..7, y=-60..60);
In this case you have a pretty good idea that there are only going to be two points (x1, f(x1)) and (x2, f(x2)) that have a common tangent line. But in order to find a and b for the equation of the tangent line, you need to know what two points have a common tangent line. That is you need to know (x1, f(x1)) and (x2, f(x2)) where the common tangent line touches the graph. To find these two points you need to know x1 and x2. You are not just finding a and b, you have to find a, b, x1, and x2. So you need four equations in this case as Robert indicated.

It is not clear to me what you are asking for. What you need to solve the problem depends on f(x). For example, if f(x) = x^2 then a tangent line at the point (c,f(c)) for any given c will not touch the graph at any other point (x,f(x)) where x is not equal to c. If f(x) = x then the tangent line at (c,f(c)) for any given point c will touch the graph at every other point (x,f(x)). Can you tell us specifically what f(x) is, or what the equation is that you were given?

It is not clear to me what you are asking for. What you need to solve the problem depends on f(x). For example, if f(x) = x^2 then a tangent line at the point (c,f(c)) for any given c will not touch the graph at any other point (x,f(x)) where x is not equal to c. If f(x) = x then the tangent line at (c,f(c)) for any given point c will touch the graph at every other point (x,f(x)). Can you tell us specifically what f(x) is, or what the equation is that you were given?

I cut and pasted in both worksheet and document mode. Seem to work fine in both.

I cut and pasted in both worksheet and document mode. Seem to work fine in both.

Robert, thanks for the reply. I knew it was only an existence theorem, but I was unsure how Maple or other CAS appoach the problem. For example, I was wondering if they first attempted to find a continuous antiderivative. I can see now that that way of thinking is a gross oversimplification of the problem in general.

Jacques, thanks for the reply. I had not really paid close attention to these issues prior to today. I mostly use Maple to do textbook type problems since I teach HS. Now I know I can't just compute an anti-derivative and take it for granted that I can apply FTC. Strangely, despite the fact that this issue has been discussed before it didn't really sink in until I read this thread in conjunction with jpmay's recent blog

A Perilous Tale of Definite Integration.

My, apologies if this seem like a simple question. Why does Maple, or any other CAS, return a discontinuous anti-derivative in situations where a continuous anti-derivative is guaranteed to exist by FTC? My problem is that I can think of some reason why this might be done but I am only guessing since I do not know for certain. (I won't bother listing any since they may be wrong)
Thanks,
Thomas