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Finding Numerical Derivatives

While the TI-84+ calculators are not symbolic manipulators (they cannot tell you the algebraic expression for a derivative), they can tell you an approximate numerical value for a derivative at a specific location.  Several methods may be used.

Method 1: using nDeriv(expression, variable, value, [e])

The nDeriv command uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line,  f ' (x) = ( f (x + e) - f (x - e)) / 2e.  As e becomes smaller, the answer becomes more accurate.
Be careful!!!   The use of this method can yield an incorrect answer at non-differentiable points. 
The default value for e is 1 E -3.

EXAMPLE: Find the numerical value of the derivative for the function stated below at the indicated location (express answer to three decimal places).
ee

Step 1:
1
  Enter the function into Y=

 

Step 2: 
2
From the HOME screen, hit the  MATH key and arrow down to choice #8 nDeriv(. 

Step 3: 

The parameters for nDeriv are expression, variable, value.  (A fourth parameter exists involving the size of epsilon and is usually left off.)
Hit ENTER .for the answer. 
 

 

Method 2: using the dy feature and the graph

Let's examine that same problem again:

Find the numerical value of the derivative for the function stated below at the indicated location (express answer to three decimal places).
fx

Step 1:
4 
Enter the equation into Y=

Step 2: 
5
Hit GRAPH.  Be sure that the WINDOW includes the x value that you will be investigating.  If not, adjust the WINDOW.
 

Step 3:
6
 Hit the MATH key and choose
#6 dy/dx. 
Hit ENTER. 

Step 4:
7
The graph will reappear.
(If more than one graph appears, use the up/down arrows to select the desired graph.)
Use the left ◄ and right ►arrows to locate the point you wish to investigate, or simply type the point.
Hit ENTER.
 

Step 5:
8
Simply type the desired value on the keypad.  The number will appear below the graph.

 

Step 6:
 9
Hitting ENTER will reveal the answer.