III. Working With A Graph

C. CALC

The CALC key menu has seven applications that can be used with a graph. The last two are used in calculus problems.

 Access the CALC MENU This is the screen.

1: value

This key can be used to evaluate the function at any value within the range [Xmin, Xmax]. It performs like TRACE key when you enter a value. You can repeat the process by entering other values. If you enter a value that is outside the range, you will get an error message.

Example 1: Enter the function shown and evaluate it at x=3 and x=-2.

 Enter the function. Use ZOOM6 Access value. When you see this screen, enter a value. Press ENTER and a value will be shown. You can repeat for other values.

2: zero

Use zero to find the x-value where a function's graph crosses the x-axis. This is an extremely useful tool in solving equations.

Example 2: Find a zero of the function shown in the first window. When you enter the left and right bounds, try to enter values that are relatively close to the zero so that other variations in the graph do not impede the process. After you enter a left bound and a right bound, the cursors shown should have the zero between them.

 Enter. Set a window. Graph. Access 2:zero. Enter a Left Bound of x=-2. Enter a Right Bound of x=-1.5. Ignore "Guess?" and press enter. This is the zero.

Note: When you are entering a Left Bound and a Right Bound, you will see two cursors. These should "box in" the area.

3: minimum

This will find the minimum value of the function over an interval that you designate with a left bound and a right bound.

Example 3: Using the function in the example above, find the minimum value of the function shown on the screen.

 Graph the function. Access "minimum". Enter the left bound. Enter the right bound. Ignore "Guess" and press enter. Minimum is at the point (-1,-4).

4: maximum

This key works exactly like the minimum key. It will find a maximum value over a given interval.

Example 4: Find the local maximum of the function shown above.

 Graph the function. Access "maximum". Enter the left bound. Enter the right bound. Ignore "Guess" and press enter. Maximum is at the point (0,-3).

Note: The minimum in the screen above shows an x value of -2.77E-6. This is the number -0.00000277 which is rounded to 0.

5: intersect

Finding where two graphs intersect can be useful in many applications, solving an equation, for example. However, if you have more than two graphs on the screen at once, it is suggested that you turn one of them off before using the intersect option. To turn off a function, move the cursor over the = sign and press enter.

Example 5: Solve the equation by using the intersect option. Find the intersection for the two functions shown.

 Enter. Use ZOOM4. CALC 5:intersect Move cursor close to point. When you see this just press ENTER. When you see this press ENTER again. This is the point of intersection. Other point of intersection.

6: dy/dx

This is a calculus application. dy/dx gives a numerical approximation of the first derivative at the indicated point. You can use trace to get to the x-value or you can enter a value of x.

Example 6: Find the numerical derivative at x=1 and x=-1.

 Enter a function. ZOOM4 CALC6: dy/dx Enter x=-1 dy/dx at x=-1 dy/dx at x=1

7: integral

This is a calculus application and gives a numerical approximation of the integral over a selected interval.

Example 7: using CALC7:integral.

 Enter a function. ZOOM4 CALC7: integral Enter x=-1 and ENTER. Enter x=1 and ENTER. Value of the integral.

 A. TRACE B. TABLE C. CALC D. Style E. FORMAT F. ZOOM