28
Math Functions
with
optional
tolerance
Classic Mode or Entry
In Classic mode or in classic edit lines, the
nDeriv(
command will paste from the
keypad or
MATH
menu.
Syntax:
nDeriv(
expression
,
variable
,
point
[,
tolerance
]
)
where
tolerance
is optional and
the default
H
is 1
E
M
5.
Example
% A
or
d
MATH
7:nDeriv(
% A
z F T
5
z
% ` z
% ` M
1
)
<
About the Numerical Derivative at a Point
The numerical derivative at a point command,
nDeriv(
or d/dx, uses the symmetric
difference quotient method. This method approximates the numerical derivative at a
given point as the slope of the secant line about the point.
( )
f
x
′
=
f x
ε
f x
ε
ε
( + )− ( −
)
2
As
H
becomes smaller, the approximation usually becomes more accurate to
approximate the slope of the tangent line at the given point x.
•
Because of the method used to calculate the numerical derivative at a point, the
calculator can return a false derivative value at a non-differentiable point.
•
Always have some knowledge of the function behaviour near the point by using a
table of values near the point (or a graph of the function).
³
Problem
Find the slope of the tangent line to the function f(x) = x
2
- 4x at x = 2. What do you
notice?
% A
z F U
4
z " "
2
<
Numerical Integral
The TI-30X Pro MathPrint™ calculates the (approximate) numerical integral of an
expression with respect to a variable
x
, given a lower limit, an upper limit and a
tolerance for the numerical method.
