More TI-89 tricks.

1. Make ti89 evaluate f(5). There are many ways to do this. Perhaps
the easiest is to switch to graphing function mode, do green diamond y=
and enter the function as y1. Say y1=x^2+2x-3. Then
input: y1(4)
output: 21

2. Make ti89 evaluate f(3,4). Swith to graphing 3D mode, do green diamond y=
and the the function as z1. say z1 = sqrt(x^2+y^2)
input: z1(3,4)
output: 5

3. Finding critical points of f(x,y). Enter f(x,y) as z1 like in #2
input: solve(d(z1(x,y),x)=0 and d(z1(x,y),y) = 0, {x,y});
output: a list of solutions.
For example if z1 = x*y*(x+y-3) = x^2y + xy^2 - 3xy
output: x = 3 and y = 0 or x = 1 and y = 1 or x = 0 and y = 3 or x = 0 and y = 0
Which list the 4 critical points (3, 0), (1, 1), (0, 3), and (0,0).

4. Faster ways of entering the command above.
A. Get the template 2nd custom(home) F3 #4 Solve and {x,y} 2nd custom
B. Move cursor to correct location, type d(z1(x,y),x)=0.
C. Highlight expression (up arrow and move cursor) copy diamond copy
move cursor diamond paste, edit the x to y.
D. enter. 

5. Taylor series, quadratic version, help
x^2+x*y^3 sto-> g(x,y)
d(g(x,y),x) sto-> gx(x,y)
d(g(x,y),y) sto-> gy(x,y)
d(gx(x,y),x) sto-> gxx(x,y)
d(gx(x,y),y) sto-> gxy(x,y)
d(gy(x,y),y) sto-> gyy(x,y)
d(gy(x,y),x) sto-> gyx(x,y)

gxy(3,4) will give the value of g_xy(3,4).

If you change g(x,y) it changes all the other g's.