IN THIS VIDEO I'LL SHOW
HOW TO USE THE TI-84 
GRAPHING CALCULATOR
TO FIND THE VALUE 
OF A DERIVATIVE
AT A GIVEN VALUE OF X.
AND WE'LL TAKE A LOOK 
AT TWO EXAMPLES.
WE WANT TO FIND THE VALUE OF THE 
DERIVATIVE OF F OF X WHEN X = 2,
AND HERE'S OUR GIVEN FUNCTION.
SO, AGAIN, OUR GOAL 
IS TO FIND THE VALUE
OF THE DERIVATIVE FUNCTION 
WHEN X = 2.
THE TI-84 CALCULATOR 
IS NOT GOING TO GIVE US
THE DERIVATIVE FUNCTION,
BUT IT WILL GIVE US THE VALUE 
OF THE DERIVATIVE
AT A GIVEN VALUE OF X.
AND THERE ARE TWO WAYS 
OF DOING THIS.
ONE WAY IS FROM THE HOME SCREEN.
SO IF WE PRESS THE MATH BUTTON,
WE WANT TO SCROLL DOWN 
TO OPTION 8 OR PRESS 8.
WE'RE LOOKING FOR THIS COMMAND 
HERE, N DERIVE OR N DERIVE.
AND PRESS ENTER, THEN WE TYPE IN 
THE RIGHT SIDE OF OUR FUNCTION.
SO WE HAVE X TO THE THIRD 
- 5X SQUARED + 2.
NOW WE HAVE TO PRESS COMMA X, 
AND THEN COMMA,
THE VALUE OF X THAT WE WANT 
TO EVALUATE THE DERIVATIVE AT,
WHICH IS 2.
CLOSE PARENTHESIS, PRESS ENTER.
A COMMON ERROR IS TO FORGET 
TO PUT THIS COMMA X
IN THE COMMAND.
NOW, THE NEXT THING IS NOTICE 
HOW IT'S GIVING US -7.999
AND SO-ON.
THE CALCULATOR'S NOT PERFECT.
WE NEED TO RECOGNIZE THIS AS -8.
SO LET'S GO AHEAD 
AND WRITE THIS DOWN
AND THEN I'LL SHOW YOU A SECOND 
WAY TO FIND THE SAME VALUE.
REMEMBER THIS WOULD BE SLOPE
WITH A TANGENT LINE
WHEN X IS EQUAL TO +2,
WHICH WE'LL SHOW IN 
JUST A MOMENT.
THE SECOND WAY TO DO THIS 
IS FROM THE GRAPH SCREEN.
SO FIRST WE'LL PRESS Y EQUALS.
NOTICE HOW I'VE ALREADY 
ENTERED THE FUNCTION IN HERE,
SO NOW I'M GOING TO PRESS GRAPH.
HERE'S THE GRAPH 
OF OUR FUNCTION,
SO FROM THIS SCREEN WE CAN 
ALSO JUST PRESS SECOND TRACE
FOR THE CALCULATION MENU.
AND THEN SELECT OPTION SIX 
FOR DY, DX.
ONCE WE SELECT OPTION 6 WE NEED 
TO TYPE IN THE X VALUE OF 2.
SO WE PRESS 2, ENTER.
AND NOTICE HOW THE DERIVATIVE 
IS EQUAL TO THE SAME VALUE
THAT WAS ON THE HOME SCREEN,
WHICH WE NEED TO RECOGNIZE 
AS -8.
OF COURSE WE COULD VERIFY THIS 
BY HAND.
F PRIME OF X 
USING THE POWER RULE
WOULD JUST BE 3X SQUARED - 10X 
AND THEN + 0.
AND THEN WE COULD JUST SUB IN 2.
SO WE'D HAVE 
3 x 2 SQUARED - 10 x 2.
WELL, THIS WOULD BE 4 x 3 THAT'S 
12 - 20, WHICH IS EQUAL TO -8.
AND, AGAIN, WHAT THIS VALUE
TELLS US IS,
GOING BACK TO THE GRAPH 
OF OUR FUNCTION, AT X = +2
OR AT THIS POINT HERE, THE SLOPE 
WITH A TANGENT LINE WOULD BE -8.
LET'S TAKE A LOOK 
AT A SECOND EXAMPLE.
WE WANT TO FIND THE VALUE OF 
THE DERIVATIVE OF OUR FUNCTION
AT THE POINT (-1,1/2).
AGAIN, HERE THEY'RE GIVING US 
THE POINT,
BUT TO DO THIS WE ACTUALLY 
ONLY NEED THE VALUE OF X = -1.
LET'S GO BACK TO OUR CALCULATOR
AND IT WILL SHOW IT BOTH WAYS 
AGAIN.
SO FROM THE HOME SCREEN 
WE'RE GOING TO PRESS MATH,
OPTION 8, ENTER.
TYPE IN OUR FUNCTION.
WE NEED TO BE CAREFUL HERE, 
WE WANT PARENTHESIS
AROUND THE NUMERATOR 
AND DENOMINATOR.
SO WE HAVE AN OPEN PARENTHESIS, 
(X - 1), CLOSE PARENTHESIS,
DIVIDED BY OPEN PARENTHESIS 
(X - 3, X, THE X VALUE'S -1),
CLOSE PARENTHESIS, PRESS ENTER.
AGAIN, THE CALCULATOR 
IS NOT PERFECT,
WE NEED TO RECOGNIZE THIS 
AS X = -0.125.
SO F PRIME OF -1 IS EQUAL 
TO -0.125 OR 0.125.
WE MAY WANT THIS 
IN FRACTION FORM,
SO IF WE GO BACK 
TO THE CALCULATOR
IT WON'T CONVERT THIS 
TO A FRACTION FOR US,
BUT IF WE TYPE IN -0.125 AND 
THEN PRESS MATH, ENTER, ENTER,
IT'S EQUAL TO -1/8, 
WHICH HOPEFULLY WE DO RECOGNIZE.
AND LETS ALSO SHOW THIS AGAIN 
USING THE GRAPH SCREEN.
SO WE'LL PRESS Y EQUALS, 
CLEAR OUT THE OLD FUNCTION,
TYPE IN THE NEW FUNCTION.
AGAIN, THESE PARENTHESIS 
ARE REQUIRED.
PRESS GRAPH, AND THEN FROM HERE 
WE PRESS SECOND TRACE
FOR CALCULATION,
AND THEN OPTION SIX.
AND THEN WE TYPE IN THE X VALUE, 
WHICH IS -1.
AND, AGAIN, NOTICE 
HOW IT'S GIVEN US -0.125,
WHICH IS EQUAL TO -1/8.
IF WE DID WANT TO VERIFY THIS 
ONE BY HAND
WE'D HAVE TO USE THE QUOTIENT 
RULE GIVEN HERE BELOW.
LET'S GO AND JUST TAKE A MOMENT 
AND DO THAT.
NOTICE OUR DENOMINATOR 
IS A DENOMINATOR SQUARED.
THE NUMERATOR IS GOING TO BE 
THE DENOMINATOR X - 3
X THE DERIVATIVE 
OF THE NUMERATOR,
WHICH IS JUST 1 - THE NUMERATOR
x THE DERIVATIVE OF THE 
DENOMINATOR, WHICH IS JUST 1.
LET'S GO AHEAD 
AND SIMPLIFY THIS.
SO HERE WE HAVE X - 3.
THIS WOULD BE - X + 1, 
SO THAT SIMPLIFIES TO -2.
SO THEN WE SUB IN -1 FOR X, 
WE'D HAVE -2/-1 - 3 SQUARED.
AND THIS ENDS UP BEING -2/16, 
WHICH IS -1/8.
AND, AGAIN, GRAPHICALLY 
WHAT THIS IS TELLING US
IS AT THIS POINT HERE 
ON OUR FUNCTION
THE TANGENT LINE WOULD HAVE 
A SLOPE OF -1/8.
LET'S GO AHEAD AND VERIFY THAT.
HERE'S THE POINT 
WE'RE REFERRING TO.
THIS RED TANGENT LINE 
DOES HAVE A SLOPE OF -1/8.
OKAY. I HOPE YOU FOUND 
THIS HELPFUL.
