# How to Find Minimum and Maximum Points With a Graphing Calculator

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You can find the maximum and minimum values of a function f(x) by graphing the function and or using calculus. The maximum and minimum values are the turning points or critical values on the graph of these functions. To locate these points, it is sometimes necessary to find first and second derivatives. The graphing calculator may be a better alternative. Read on to learn more.

### Things You'll Need

• TI-83 Plus graphing calculator
• Select a function to solve. As an example, use Y1 = x² -6x+5.

• Turn on the calculator and press "Y=" key. You see a list of Y values (Y1 to Y7).

• Input the equation for Y1 by entering the following keys:

"X,T, θ, n", "x²", " -", "6", "X,T, θ, n", "+" and "5" keys.

• Press the "Graph" key. The graph is of a parabola, which is concave upward, so you need to find the minimum value. If a graph is concave downward then find the maximum value.

• Hit the "2nd" and "Trace 3" keys. The calculator displays the words "Left Bound" on the screen. Choose a left boundary for the minimum value by moving the cursor with the left arrow key to the left of the minimum point and then press the "Enter" key.

• Select a right boundary for the minimum value when the calculator displays the words "Right Bound" on the screen. Use the right arrow key to move the cursor to the right of the minimum point and press the "Enter" key.

• Estimate the location of the minimum value when the calculator asks for a guess. Use the arrow keys to move the cursor near the minimum point and hit the "Enter" key. The resulting point is X=3.0000007 or X= 3, Y= -4. Please note that if you get a value such as 3.0000007 the actual answer is 3. Check this by substituting it into the equation.

## Tips & Warnings

• The directions given here are for a TI-83 Plus calculator. Please see the Resources to learn about graphing with some other models.
• Note that to find the minimum point in Step 5, you press "2nd" and "Trace 3" keys, but to find a maximum point you choose "2nd" and "Trace 4" from the menu.
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