how to find relative maximum

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)

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.