Calculator Skills
You need to be able to find or do:
1. zeros
2. max/min
3. numerical derivatives and numerical integrals (numerical integrals start in Chapter 5)


From Home Screen
On a Graph
4. where graphs intersect (this can be used to solve equations)
5. graph a derivative function
On the TI-84:
To find zeros, put your expression into y# (to graph). Graph your function. Go to Calc (above trace) and
choose zero. Put your cursor left of the x-intercept (hit enter), then put your cursor right of the xintercept (hit enter). (You are giving the calculator the boundaries to find the answer between
boundaries) You never guess, so hit enter.
To find max/min, put your expression into y# (to graph). Graph your function. Go to Calc (above trace)
and choose maximum or minimum. Put your cursor left of the max/min (hit enter), then put your cursor
right of the max/min (hit enter). (You are giving the calculator the boundaries to find the answer
between these boundaries) You never guess, so hit enter.
To find numerical derivatives from the Home Screen, go to Math, nderiv( and fill in
If you have the expression already in y# (to graph), then you can type
d
(expression) x  # .
dx
d
( ywherever you put the epression ) .
x#
dx
To get ywherever you put the epression , you can go to Vars, move over to y-vars, Function, and choose
ywherever you put the epression . This gets you a derivative value at an x-value.
To find numerical derivatives on a Graph, go to y  and put your expression in y# to look at the graph.
When the graph is on your screen, you can calculate the derivative by going to Calc (above trace) and
choose
dy
and then type the x-value where you want the derivative value.
dx
To find where graphs intersect, go to y  and put your expressions in y# and ydifferent # . Go to Calc
(above trace) and choose intersect. Put your cursor on 1 graph, hit enter. Put your cursor on the other
graph, hit enter. You never have to guess, so hit enter. This gives you the coordinates of the
intersection point. If you want to store the x-value in a letter, go to the home screen, hit STO and then
choose the alphabetical letter in which you would like to store this value (i.e. Alpha 8 to store in P). If
you wanted the y-value of the intersection point, go back to your home screen and hit y (alpha 1)
ENTER. You can now store that value in whatever alphabetical letter in which you choose. You could
solve 4 x 2  2 x  7 or f ( x )  3 with this technique.
To graph a derivative, you can go to y  . Then go to Math, go to nderiv( and put
d
(expression for f(x)) x  x If you wanted to solve f ( x)  3 , you could graph f ( x ) in y# . This
dx
d
(expression for f(x)) x  x in y# and 3 in ydifferent # and find where they intersect.
could be
dx
To find the numerical integral, from the home screen, go to Math, go to fnInt, and then fill in the boxes
with the lower limit, the upper limit, the function, and d(variable). This is the most accurate method.
To find the numerical integral, with a graph on your screen, go to Calc (above trace) and choose
 f ( x) dx , and then type in the lower and upper limits of integration.
***Make sure your calculator is set for Radians during Calclulus. This can be done by hitting the Mode
button.
On the Casio fx-CG50:
To find zeros, go to Menu Graph, put your expression into y# (to graph). Hit EXE. Graph your function
by hitting Draw (F6). Go to G-Solv (above F5) and choose root. You can move your cursor left and right
to see the x-intercept(s).
To find max/min, go to Menu Graph, put your expression into y# (to graph). Hit EXE. Graph your
function by hitting Draw (F6). Go to G-Solv (above F5) and choose either Max or Min. You can move
your cursor left and right to see the max(s) or min(s).
To find numerical derivatives from the Home Screen, go to Math (above F4),
d
(above F4) and fill in
dx
d
(expression) x  # . If you have the expression already in y# (to graph), then you can type
dx
d
( ywherever you put the epression ) . To get ywherever you put the epression , you can go to Vars, Graph (F4), Y (F1) and
x#
dx
choose the # wherever you put the expression. This gets you a derivative value at an x-value.
To find numerical derivatives on a Graph, go to Math Graph, put your expression in y# to look at the
graph. When the graph is on your screen, you can calculate the derivative by hitting F4, choose Tangent
(F2), and then hit the x-value where you want the derivative value. Hit EXE. This will draw the tangent
line and give you the value for
dy
.
dx
To find the numerical integral, from the home screen, go to Math (F4) , move over with the arrow (F6),
and choose
 dx (F1).
Fill in the boxes with the lower limit, the upper limit, and the function. This is
the most accurate method.
To find the numerical integral, with a graph on your screen, go to G-Solv (F5), move over with the arrow
(F6), choose
 dx (F3), and then choose  dx again (F1). Type in the lower and upper limits of
integration.
To find where graphs intersect, go to Menu Graph, put one expression into y# (to graph) and the other
into ydifferent # . Hit EXE. Graph your functions by hitting Draw (F6). Go to G-Solv (above F5) and choose
either Intersect. You can move your cursor left and right to see where to graphs intersect if there are
multiple places. If you want to store this value in a letter, use the MENU button to take you back to the
Run-Matrix Home Screen. The x-value of the intersection is stored in x, so if you hit x (x, theta, T) and
EXE, the number is on your home screen. Now you can store in a different letter by using the RIGHT
ARROW button and then choose the alphabetical letter in which you would like to store this value (i.e.
Alpha 4 to store in P). If you wanted the y-value of this intersection point, the y-value of the intersection
is stored in y, so if you hit Y (alpha -) and ESE, the number is on your home screen. Now you can store in
a different letter by using the RIGHT ARROW button and then choose the alphabetical letter in which
you would like to store this value. You could solve 4 x 2  2 x  7 or f ( x )  3 with this technique.
To graph a derivative, you can go to Menu Graph. Then hit the button Optn, choose Calc (above F2),
d
d
(expression for f(x)) x  x . If you wanted to solve f ( x)  3 , you
(above F1) and then fill in
dx
dx
d
(expression for f(x)) x  x in y# and 3 in ydifferent # and find
could graph f ( x ) in y# . This could be
dx
where they intersect.
***Make sure you have turned on derivative in Setup (above Menu). Make sure you calculator is set
for Radians during Calculus. This can be set in Setup (above Menu).