Using the TI-84 Effectively (AP Calculus AB)

Using the TI-84 Effectively (AP Calculus AB)

The weighted vest comes off today!

Today, we will cover how to...

• Find the roots of a polynomial by graphing

• Find local maximum and minimum of any graph

• Find the value of a derivative at any point

• ...essentially having the calculator do the HEAVY LIFTING FOR YOU!

The Best Button you never knew existed...

• Hit "2nd"

• Then "Trace"

• You have now unlocked the "Calculate" Menu!

• Notice all the Calculus things that are there... (6 and 7)

• Today, we will focus on selections 2, 3, 4 and 6.

Multiple Choice

How do you access the "Calculate" Menu on the TI-84 Calculator?

• "2nd" + "Trace"

• "MATH"

• "2nd" + "Graph"

• Pray to the calculus gods and Sir Isaac Newton for answers

Finding Roots (x-intercepts) of a function

• Remember: x-intercepts are where y = 0, have ordered pair (x, 0)

• Use the function y1 =  $x^2-4x-4$  

• Go to the Calculate Menu, and select (2) "Zero"

• find the "left bound" by hitting the "<-" until the cursor is left of the first x-intercept and hit "Enter"

• find the "right bound" by hitting the "->" until the cursor is right of the first x-intercept and hit "Enter"

• "Guess" what the value of x will be 

• Your left most x-intercept should be (-0.828, 0)

Open Ended

Find the right most x-intercept of y1 =

 $x^2-4x-4$  

Finding Maximum and Minimum of a Graph

• Let's use a different function for this ...

• In place of Y1, use the function $x^3-4x+2$  (check the exponents!)

  
  

Finding Maximum and Minimum of a Graph

• Go to the "Calculate Menu" and select (3) "Minimum"

• For this particular function, the local min is found at the right between 0 and 2.

• The process is the same as finding the zeros: Left Bound, Right Bound, Guess.

• Just make sure you know which value you are finding, otherwise the calculator will return an "Error"

• The local min of this function is (1.155, -1,079)

Open Ended

Find the Local Maximum of Y1 =

 $x^3-4x+2$  

Using (6) dy/dx

• The TI-84 is not able to derive a function explicitly...

• ... but it can help you find the rate of change at any point on a graph!

Finding dy/dx of a function

• Let's use a new function...

•  Y1 =    $\sqrt{\left(x+2\right)^2+10}$  

• Enter the "Calculate" Menu and Select (6) dy/dx

• You will be prompted for a value for x. Type in "0" to find the value of the derivative of Y1 at x = 0.

Open Ended

Find dy/dx of Y1 = 3*tan(x) + 2 at x = 0

Let's dive into Applications of Derivatives!

You are READY!