Calculus for Business
Tech Assignment C-Numerical Derivatives &
Definite Integrals
Name:____________________________________
Date:_____________________________________
PART 1:
Sometimes finding the derivative of a function can be a real pain (algebraically). This is often the case with
rational functions because you would need to use either the quotient rule or the chain rule. If you need to find
the derivative at a particular value, the calculator becomes a very important resource. This activity will help
you to be able to use your calculator to find a particular derivative. This comes in handy when using the first
derivative test also…
EXAMPLE:
Graphing a Derivative
CALCULATOR FUNCTION: MATH 8  nDeriv(function,X,X).
x 1
. You can use the graph of the derivative to
x2  4
determine where the function is increasing (derivative is positive) and where it is decreasing (derivative is
negative) and where it has a maximum or minimum (where the derivative is zero or undefined). The graph of
the derivative may take a few moments to draw. This is because the calculator is using numerical approximation
techniques to determine the derivative values.
Example: Graph the derivative of the function f ( x) 
Step 1:
Enter the function in y1 and the derivative in y2.
Step 2:
Hit ZOOM 6 to give a standard window. In this case it shows that the functions are very close to
the x-axis so we must adjust our window:
Step 3:
Use the thick curve option to help distinguish between the original function and the derivative.
Step 4:
Use either the table or value functions to identify y2 when x is a particular value.
Example: f ' (2)  ?
Result: 0.625
1
Use the process described in PART 1 to complete the following:
1.
Step 1:
f ( x)  x 2  2 x  1
Enter the function in y1 and the derivative in y2.
Plot1 Plot 2 Plot 3
\ Y1 
\ Y2 
Step 2:
What window did you use?
WINDOW
Xmin=
Xmax=
Xscl=
Ymin=
Ymax=
Yscl=
Xres=
Step 3:
Step 4:
Give a rough sketch of the original function and the derivative based on your selected window.
f ' (2) 
2
Part 2:
A definite integral is the area in a coordinate axis bounded by the function, the x-axis, and two particular and
two vertical lines. Again, it may be too cumbersome to determine integrals by hand so we need a graphing
calculator approach.
4
Example:
Find
 x dx
2
0
Step 1:
Enter the function in y1
Plot1 Plot 2 Plot 3
\ Y1  x 2
\ Y2 
Step 2:
Determine a reasonable window. Should be consistent with lower and upper bounds.
WINDOW
Xmin=
Xmax=
Xscl=
Ymin=
Ymax=
Yscl=
Xres=
Step 3:
Give a rough sketch of the original function and the shaded area based on your selected window.
4
Step 4:
 x dx =
2
0
3
Use the process described in PART 2 to complete the following:
2
Find
 2x
2
 8 dx
2
Step 1:
Enter the function in y1
Plot1 Plot 2 Plot 3
\ Y1 
\ Y2 
Step 2:
Determine a reasonable window. Should be consistent with lower and upper bounds.
WINDOW
Xmin=
Xmax=
Xscl=
Ymin=
Ymax=
Yscl=
Xres=
Step 3:
Give a rough sketch of the original function and the shaded area based on your selected window.
2
Step 4:
 2x
2
 8 dx =
2
4