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Maximum and Minimum Values

EXAMPLE: Examine the function y = x3 - 3x + 1.
(Three methods will be shown.)

Method 1: (Graphical)



• Enter function into f1(x).

, #6: Analyze Graph, #2, Minimum or
#3 Maximum

• Move cursor to left of peak (or valley), press
(lower bound)
You will see a movable vertical dotted line.

• Move cursor to right of peak (or valley) press
(upper bound)
You will see gray shading and a second vertical line.

• The word maximum (or minimum) will appear on the screen highlighted in yellow, along with the coordinates of the point.

• Coordinates are displayed on screen.
Maximum: (-1,3)
Minimum: (1,-1)



 


Method 2: (Graphical Trace)



• Enter function into f1(x).

, #5: Trace, #1, Graph Trace

• Using left and right arrow keys, move cursor along the graph.
A spider looking icon will move along the graph when using the left and right arrows.

• As you approach a peak or valley, the calculator will automatically grab the "special" point and display a yellow highlighted maximum or a highlighted minimum near the point, with the coordinates showing in the lower right corner of the screen.

• If you want the coordinates placed on the max or min,
hit when you find the max or min.

• Maximum: (-1,3)
Minimum: (1,-1)

• To exit the Trace tool, hit (escape).

 

 

 

 

Method 3: (Numerical)

(Calculator Page)

, #4: Calculus, #6, Numerical Function Maximum

nfMax( will be pasted on the screen.

nfMax(Expression, Variable, Lower Bound, Upper Bound)

Max at x = -1
Min at x = 1

This method yields the x-value only. To find the y-value, substitute the x-value back into the function.




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