I tried one of the problems I gave to student in Maxima, and failed. You
have to minimize the following (a shortest path problem between (0,0) and
(3,1) with the side condition, that you can travel faster along the x-axis -
I teach beginner classes this year):
ea : a/15+sqrt((3-a)^2+1)/10
2
a sqrt((3 - a) + 1)
(%o1) -- + ------------------
15 10
solve(diff(ea,a)=0,a)
2
2 sqrt(a - 6 a + 10) - 9
(%o2) [a = - -------------------------]
3
Of course, it is quite easy to solve this by hand, or guiding Maxima to
solve it. But is there any way to find the soluton automatically in Maxima?
By the way, this equation has the interesting property, that you get a false
solution, if you do it by hand the usual way, isolating the sqrt, squaring
and solving.
R. Grothmann
PS: I take this opportunity to thank Maxima for existence, and those
maintaining it. It has been of great value for my Euler program.