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Finding Maxima and Minima
(Extrema)

When studying relative (local) maxima and minima of graphs, the graphing calculator may be used to find these values.  Several methods may be used.

 

Method 1: (using the CALCULATE Menu)

Locate the relative maximum/minimum for the function
                     .

Step 1:

  Enter the equation into Y=

 

Step 2: 

Adjust the WINDOW to coincide with the given domain.  Hit GRAPH.  Be sure the graph is viewable in the graphing window.  Adjust accordingly. 

Step 3: 

Let's find the maximum value first.  Under the CALC (2nd TRACE) menu, choose #4 maximum. 
Hit ENTER
 

Step 4:

When asked for Left Bound, move the cursor (use arrow keys) to the left of the observed maximum location.  Hit ENTER.  You will see a mark indicating that you have "locked" this position. 

Step 5:   When asked for Right Bound, move the cursor (use arrow keys) to the right of the observed maximum location.  Hit ENTER.  You will see a mark indicating that you have "locked" this position.

Step 6:
 
When asked for Guess, simply hit ENTER. 

Step 7:

The coordinates of the maximumm value (within your marked boundaries) will appear.
ANSWER:  
 Max (2.029, 1.920)


f

  Note:
 
If you are investigating more than one location on a graph, you must start this process from the beginning for each point being investigated.                            (Return to Step 3.)


 This same process is used to examine relative minima.
(#3: minimum)
ANSWER:  Min(4.913, -4.814)

 

 

Method 2: (using the fMin and fMax functions)

Investigate relative minima/maxima for .

Step 1:

  Enter the equation into Y=

Step 2: 

Hit GRAPH.  Be sure the graph is viewable in the graphing window.  Adjust the WINDOW if needed.

Step 3:

From the HOME screen, hit the MATH key.  Choose either #6 fMin or #7 fMax. 
Hit ENTER

Step 4:

The parameters for fMin and fMax the same:
fMin(expression, variable, left bound, right bound)
Be careful:  The answer from fMin is the X-coordinate where the minimum occurs.  It is not the actual y-value minimum.   You must then calculate the y-value.

Step 5:

Again, remember that the answer from fMax is the X-coordinate where the maximum occurs.  You must then calculate the y-value.

HINT:  To get Y1(Ans):
   Y1:   VARS -> Y-VARS -
             #1Function
   Ans:   2nd (-) key

 

 

 

ANSWERS:

Min(5.070, -7.759)

Max(.263, 6.129)



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