If you’re studying calculus or any advanced math course, you will certainly come across the concept of stationary points.
So, what is a stationary point? A stationary point is a point where the derivative of a function is zero, indicating that the slope of the graph is neither positive nor negative. A stationary point is important because it can indicate a local maximum or minimum of the function (also known as maxima or minima)
In finding the y-value of stationary points, a graphing calculator such as TI-84 Plus CE can come in handy. Here’s a step-by-step guide on how to find the y-value of stationary points with TI-84 Plus CE. You might also enjoy reading IB Maths Vs. A-Level Maths – Which One is Harder?
Step 1: Graph your Function
Before you can start finding the y-value of stationary points, you need to enter the function you’re working with into the calculator.
To do this, press the “Y=” key on your calculator and enter the function as you would write it in your notebook. Make sure you use the “X” key to represent the independent variable. Then press the “Graph” button, and you should be able to visually identify any stationary points on the curve.
Step 2: Find the Derivative
The next step is to find the derivative of the function which can be done using the “Calc” button on the calculator.
And then select “Derivative” and enter the function you’ve graphed. The calculator will automatically find the derivative of the function.
Step 3: Find the X-Value of Stationary Points
Once you’ve found the derivative of the function, you can find the x-value(s) of the stationary point(s), which can be found by solving the derivative equal to zero. You can find the x-value(s) of the stationary point(s) using the “Solve” function on the calculator.
Another way to find the stationary points is to look for spots where your Trace function “pauses” on the graph. When the Trace function pauses, you’ll see a blinking cursor on the graph, indicating a stationary point. If you missed the pause, you can use the left or right arrow keys to backtrack on the graph and find the blinking cursor.
Step 4: Plug in X-Value to Original Function
Now that you’ve found the x-value(s) of the stationary point(s), you can plug them into the original function to find the respective y-value(s), which can be done by selecting the original function, entering the x-value(s) you found in step 3 and pressing the “Enter” button. Your calculator will then display the corresponding y-value(s) on the screen.
Alternatively, you can read the Y-value of the stationary point. Once you’ve found the blinking cursor (or the stationary point), read the y-coordinate corresponding to the x-coordinate of the stationary point. The y-coordinate will be shown on the bottom of the screen, right next to the x-coordinate. This y-coordinate represents the y-value of the stationary point.
Step 5: Confirm the Type of Stationary Point
After finding the y-value of the stationary point, you need to confirm whether it’s a maximum or minimum point. One way to do this is by looking back at the graph and checking the shape of the curve around the stationary point.
- If the slope of the curve changes from negative to positive, then the stationary point is a minimum point.
- If it changes from positive to negative, it’s a maximum point.
Step 5: Verify Accuracy
It is important to remember that the TI-84 Plus CE calculator is a tool. While it can be helpful in finding stationary points, it is always important to verify the accuracy of your results.
You can verify your results by analyzing the graph of the original function as well as the graph of its derivative. In addition, I encourage you to manually calculate the derivatives and verify your results using the calculator.
What to read next:
- Chain Rule: Definition and examples.
- How to Find Vertical Asymptotes of Rational Functions!
- How to Find the Horizontal Asymptote: With examples!
- 9 Best YouTube Channels to Learn Calculus.
Finding the y-value of stationary points is a crucial step in calculus and can help you determine the maximum or minimum points of a function. Using a graphing calculator such as TI-84 Plus CE can make this task easier and faster, allowing you to shift your focus to other important concepts.
I believe that by following the above steps, you can quickly find the y-value of stationary points. I also encourage you to always verify the accuracy of your results by learning to manually find the nature of stationary points.