Expression Examples
This page contains examples for the "solve(y)", "dxdy(x)", "intg", "maxY", "minY", and "exprna=b" keys from the Expression Calculator.
Solving using the "solve(y)" key.
The "solve(y)" key will solve for the rgx value between x1 and x2 that will will result in the value entered.
Find the root of:
(rgx+3)×(rgx-1)^2
from rgx = -4 to 0, and then from 0 to 2.
| Value | Keystrokes | Display | Description |
|---|---|---|---|
| C | Clears the expression. | ||
| (rgx+3)×(rgx-1)^2 | Enter the expression to solve. | ||
| K | Enters K mode. | ||
| -4 | STO x1 | -4.00 | Stores the x1 value. |
| 0 |
STO x2 | 0.00 | Stores the x2 value. |
| 0 | solve(y) | -3.00 |
Solves for the value of rgx between x1 and x2 that evaluates to 0. |
| -4 | solve(y) | -3.22 |
Solves for the value of rgx between x1 and x2 that evaluates to -4. |
| 0 | STO x1 | 0.00 | Stores a new x1 value to find another root |
| 2 |
STO x2 | 2.00 | Stores a new x2 value. |
| 0 | solve(y) | 1.00 |
Solves for the value of rgx between x1 and x2 that evaluates to 0. |
By plotting the expression you can see the approximate values of the roots.
Calculate a derivative by using the "dydx(x)" key.
Find derivative of:
(rgx+3)×(rgx-1)^2
at rgx = 0.
| Value | Keystrokes | Display | Description |
|---|---|---|---|
| C | Clears the expression. | ||
| (rgx+3)×(rgx-1)^2 | Enter the expression to plot. | ||
| K | Enters K mode. | ||
| 0 | dydx(x) | -5.00 | Calculates dydx of the expression at x = 0. |
Integrate an expression using the "intg" key.
Using the Expressions calculator, use the "intg" key to integrate the expression:
(rgx+3)×(rgx-1)^2
from rgx = -3 to 1.
| Value | Keystrokes | Display | Description |
|---|---|---|---|
| C | Clears the expression. | ||
| .2×rgx^3-2×rgx+6 | Enter the expression to plot. | ||
| K | Enters K mode. | ||
| 4 | STO xMax | 4.00 | Stores the max value the plot. |
| +/- STO xMIN | -4.00 | Stores the min value the plot. | |
| -3 |
STO x1 | -3.00 | Stores the x1 value. |
| 1 |
STO x2 | 1.00 | Stores the x2 value. |
| intg | 21.3 |
Calculates the integral. |
Pressing the "shade P" key will display the plot with the integral shaded.
The History item:
Numerical Integration of expression from x1 to x2.
Expression:
(rgx+3)×(rgx-1)^2
-3.00 : x1
1.00 : x2
0.0000000100 : max error
4.00 : steps
21.3 : result
For some expressions you may want to change the max error or steps. These values can be changed in the "% Integrate prefs" data item found in the Data Manager.
Find the value of rgx for the maximum value of an expression using the "maxY" key.
You have a product that you sell 75 of per month at $15 each. Research has determined that for every $1 increase in price, 3 fewer units will be sold. What price increase will maximize revenue?
Enter the expression for revenue: (75-3×rgx)×(15+rgx)
from rgx = -3 to 1.
| Value | Keystrokes | Display | Description |
|---|---|---|---|
| C | Clears the expression. | ||
| (75-3×rgx)×(15+rgx) | Enter the expression for revenue. | ||
| K | Enters K mode. | ||
| 0 | = | 1,125 | Calculates the current revenue for a 0 price increase. |
| 0 | STO x1 | 0.00 | Stores the x1 value. |
| 10 |
STO x2 | 10.00 | Stores the x2 value. |
| shift maxY | 5.00 |
Calculates the value of rgx (the price increase) for the maximum value of the expression. | |
| = | 1,200 |
Calculates the maximum value of the expression, the new revenue. |
Find the value of rgx for the minimum value of an expression using the "minY" key.
Using the Expressions calculator, use the "minY" key to find the value of rgx for the minimum value of:
(rgx+3)×(rgx-1)^2
from rgx = -1 to 2.
| Value | Keystrokes | Display | Description |
|---|---|---|---|
| C | Clears the expression. | ||
| (rgx+3)×(rgx-1)^2 | Enter the expression. | ||
| K | Enters K mode. | ||
| -1 | STO x1 | -1.00 | Stores the x1 value. |
| 2 |
STO x2 | 2.00 | Stores the x2 value. |
| shift minY | 1.00 |
Calculates the value of rgx for the minimum value of the expression. | |
| = | 5.39E-26 |
Calculates the minimum value of the expression. In this case, 0. |
In this case, the minY value of 1.00 can be rounded using the "shift RND" key. Then pressing "=" will give the result of 0.00.
Calculating the value of rgx where two expressions are equal using the "exprna=b" key.
Using the Expressions calculator, use the "exprna=b" key to find the value of rgx where the following expressions are equal:
(rgx+3)×(rgx-1)^2
rgx^3
from rgx = -2 to 2.
| Value | Keystrokes | Display | Description |
|---|---|---|---|
| C | Clears the expression. | ||
| (rgx+3)×(rgx-1)^2 | Enter the expression. | ||
| STO exprna | Stores the expression as exprna | ||
| C | Clears the expression. | ||
| rgx^3 | Enter the expression. | ||
| K | Enters K mode. | ||
| STO exprnb | Stores the expression as exprnb | ||
| 2 | STO x2 | 2.00 | Stores the x2 value. |
| +/- STO x1 | -2.00 | Stores the x1 value. | |
| exprna=b | 0.697 |
Calculates the value of rgx where the expressions are equal. | |
| = | 0.339 |
Calculates the result of the expressions where they are equal. |
The history details:
Calculates the value of x where expression a = expression b
between x1 and x2.
Expression a: (rgx+3)×(rgx-1)^2
Expression b: rgx^3
-2.00 : x1
2.00 : x2
Result: 0.697
Entering 2 and pressing the "plot(n)" key will display a plot of the expressions.
