General - Graph Maximum and Minimum

Step 1:

Enter the equation into Y=

Step 2:

Hit GRAPH.
It may be necessary to adjust the WINDOW so you can see the "hills" and "valleys".

Step 3:
mm3
This graph has a "valley", so look for the minimum. Under the CALC (2nd TRACE) menu, choose #3 minimum.
Hit ENTER.

Step 4:

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

Step 5: mm5 When asked for Right Bound, move the cursor (use arrow keys) to the right of the observed minimum location. Hit ENTER. You will see a ◄ mark indicating that you have "locked" this position.

Step 6:
mm6
When the last screen asked for Guess, simply hit ENTER.

Step 7:

The coordinates of the miminum value (within your marked boundaries) is:
Min (2, 1)

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 maxima.
In step 3, choose #4: maximum.

METHOD 2: 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:
rounded to nearest thousandths

Min(5.070, -7.759)

Max(0.263, 6.129)