HP 40gs User Manual page 209

TABVAR
TAYLOR0
Computer Algebra System (CAS)
1 1 –
4
⋅ ⋅
----- - h ----- - h
+
16 8
Variation table
TABVAR has as a parameter an expression with a
rational derivative.
TABVAR returns the variation table for the expression in
terms of the current variable.
Typing:
2
TABVAR(3X -8X-11)
gives, in step-by-step mode:
2
( ⋅ 8 x ⋅
F = 3 x –
( ⋅ ⋅
F' = 3 2 x 8 –
→ ( ⋅ ( ⋅
2 3 x 4 –
Variation table:
–∞
–
4
-- -
3
+∞
–
49
↓
--------- -
3
The arrows indicate whether the function is increasing or
decreasing during the specified interval. This particular
variation table indicates that the function F(x) decreases
for x in the interval [–∞,
4
at x = . It then increases in the interval [ , +∞], reaching
-- -
3
a maximum of +∞.
Note that "?" appearing in the variation table indicates
that the function is not defined in the corresponding
interval.
Limited expansion in the vicinity of 0
TAYLOR0 has a single argument: the function of x to
expand. It returns the function's limited 4th-relative-order
expansion in the vicinity of x=0 (if x is the current
variable).
1
3 2
⋅ (
-- - h
+ + h + 0 h
2
)
– 11
)
) )
+ +∞ X
+∞ F
↑
4
], reaching a minimum of
-- -
3
5
) ( )
h = x
–
49
--------- -
3
4
-- -
3
14-27