Calculus with the TI-84
Please note that the TI-84 uses numerical approximation methods for calculus. The results are often not
exact, though the approximations have a high level of accuracy.
From the graph of a function:
Sketching a tangent line:
Using the DRAW menu, you can draw a tangent line to a curve at a particular value of x. Push 2nd PRGM
for DRAW, then select 5: Tangent
You will be returned to the graph. You may move the cursor left or right to a likely location, or just enter
the x value of the point where you wish to draw the tangent line.
The tangent line will be drawn and its equation provided.
Calculating a derivative:
You may calculate the value of the derivative of a graphed function at a point.
Push 2nd TRACE to access the CALCULATE menu, then select 6:
dy
dx
You may move the cursor left or right to a location you like, or just enter the x value of the point where you
wish to calculate the value of the derivative.
Computing a definite integral, and sketching the corresponding area:
You may calculate the value of a definite integral of a graphed function.
Push 2nd TRACE to access the CALCULATE menu, then select 7:
 f (x)dx
You may use the cursor to trace to the left (a) value (called lower limit) and then the right (b) value (upper
limit), or you may enter the x values you wish to use for a and b to both calculate

b
a
f (x)dx and draw the
areas related to the integral.
Note: to clear drawings, you choose 1: ClrDraw from the DRAW menu. Drawings will also be cleared if
you change your viewing rectangle or your function definition in Y=
Copyright 2007. Concepts of Calculus for Middle Level Teachers. Math in the Middle Institute Partnership, University of Nebraska, Lincoln.
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From the home screen:
Calculating the derivative of a function at a point:
You may calculate the value of the derivative of a function at a point.
Push MATH , then select 8: nDeriv
The syntax is: nDeriv(function, variable, value). If f (t)  3et and you want the value of f (5.2) , you enter
nDeriv( 3et , t, 5.2), and your calculator returns the value 543.817, which is the approximate value of 3e5.2 ,
the actual value of the derivative.
Computing a definite integral:
You may calculate the value of a definite integral of a function from x = a to x = b.
Push MATH , then select 9: fnInt
The syntax is: fnInt(function, variable, a value, b value). If you want the value of

3
2
x 5 dx , enter
36 2 6
 , which is the exact value of
fnInt(x , x, 2, 3). Your calculator will return the approximate value of
6
6
5
the definite integral.
To draw the graphs of derivatives and integrals of functions:
Sketch the graph of a derivative function:
To draw the graph of the derivative of a function, first enter the function in Y1. Graph the function, making
sure that you have a good viewing rectangle.
Then in Y2 enter nDeriv(Y1, x, x). (Remember that nDeriv is found in the MATH menu. Y1 is found in
VARS, then arrow right to Y-Vars, then choose 1:Function, and then the function number for which you
wish to graph the derivative.)
Push GRAPH . The calculator will graph both the function and its derivative. The graph of the derivative
will be rather slow, since the calculator must calculate the numeric value of the derivative of each value of
x for which it plots a point.
Sketch the graph of an anti-derivative:
To draw the graph of an indefinite integral of a function, first enter the function in Y1. Graph the function,
making sure that you have a good viewing rectangle.
Copyright 2007. Concepts of Calculus for Middle Level Teachers. Math in the Middle Institute Partnership, University of Nebraska, Lincoln.
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Then in Y2 enter fnInt(Y1, x, a, x). (Remember that fnInt is found in the MATH menu. You will need to
choose a value for a. Since an indefinite integral is an entire family of antiderivatives generated by using
different values for the constant C, the value you pick for a will determine which of the antiderivatives
your calculator will graph. The point (a, 0) will be on the graph.)
Push GRAPH . The calculator will graph both the function and one of its antiderivatives. The graph of the
antiderivative will appear rather slowly, since the calculator must calculate the numeric value of the
definite integral from a to x for each value of x for which it plots a point.
To use the programs AREA and INTEGRAL:
The AREA program illustrates the rectangles for the Left Sum and gives the numeric approximation, then
illustrates the rectangles for the Right Sum and gives the numeric approximation.
The INTEGRAL program does not illustrate the areas being calculated, but gives values for the Left Sum,
the Right Sum, the Trapezoid Rule (average of Left and Right Sums, or geometrically, draw a trapezoid for
each subinterval), the Midpoint Rule (uses the function value at the midpoint of each subinterval to
determine the heights of the rectangles, and Simpson’s Rule (fits a parabola to the 3 function values at the
beginning, middle, and right of each TWO subintervals).
For the INTEGRAL program, please use an even number subintervals. Otherwise, the Simpson’s Rule
approximation will not be correct.
Both of the programs require that the function you wish to integrate to be entered into Y1. For the AREA
program, you will also need to be sure that a suitable viewing rectangle has been selected.
From the home screen, Push PRGM to access PROGRAM. Select the program you wish to use and push
ENTER .
Each program has pauses built in so that you can view the results of each part. To move to the next part,
push ENTER.
Copyright 2007. Concepts of Calculus for Middle Level Teachers. Math in the Middle Institute Partnership, University of Nebraska, Lincoln.
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