Curve Sketching

This section is currently under construction.

1. How can I find the coordinates of inflection points with the calculator? I try tracing but don't really know if I am on or near the inflection point.

Answer. If you suspect an inflection point for a function Y₁ in an interval, graph the second derivative in that interval. If the graph crosses the x-axis, you have a point of inflection where it crosses the x-axis. To graph the second derivative, you can either compute it using calculus, or ask the machine to graph nDeriv Y₂, where Y₂ is nDeriv Y₁. Recall that the syntax for the numerical derivative of Y₁ is nDeriv(Y₁,X,X). This can be accessed by pressing the following buttons: [MATH][8] [VARS][-->] [1][1][,][X][,][X][)]

2. I try graphing y=(x^2-1)/(x-1) . The teacher says I should get something that looks like a line but I don't. What am I doing wrong?

Answer: You most likely left out the parentheses on the top and bottom of the fraction.

3. My screen shows that my two graphs intersect in two points, but each time I try to calculate the intersection, I always get the first intersection point. Why can't I get the second intersection point?

Answer: This can happen for many reasons. One way around this, when trying to find where f(x)=g(x), is to graph f(x)-g(x) and see where that crosses the x axis. That is, find where f(x)-g(x)=0. These are solutions of f(x)=g(x). Sometimes it is easier to see the zeroes of f(x)-g(x). You can either zoom in on the zeros to find them, or use the zero finding capability of the calculator ([2nd] [TRACE][2]). Your manual or teacher can show you how to complete finding the zeros. Another technique is this: When using the intersection command and you are asked for a "guess", pick a value much larger than what you took to get the first intersection point. Sometimes that will do it. A third way is to keep trying different values for the "guess" until you finally get the answer.

4. How do I stop the machine from graphing while it is graphing?

Answer: Press [2nd][ON]. This will stop the graphing in its tracks. This is not a pause.

5. I am in the standard window and want to get the cursor to the point on the curve where x=9. So I press trace and then the right arrow button a million times. Isn't there a faster way to get there?

Answer: Yes. When you are on the graphing screen just press the [trace] button followed by the number [9]. The cursor immediately is moved to a point whose x coordinate is 9. To jump from there to 7, just press [7]. (You don't have to press trace again if you haven't left the graphing screen.) This will only work if the x value that you want to jump to is on the screen you are in. If you are working in the standard window where xmax is 10 and you press [11] in an attempt to jump to 11, it won't work. You will get an error.

6. I entered the expression (X^2)*(Y^3) into the Y₁ function variable. I then went to the home screen and stored the number 2 into Y. Next, I pressed [GRAPH], expecting to get the graph of 8*(X^2). Instead, I got the message "ERROR: INVALID". What happened?

Answer: For purposes of graphing or creating tables, the TI83 does not allow the use of the variable Y in an expression for a function. Thus, use a different variable, such as Z, instead of Y. Then, if we set the fuction Y₁ equal to (X^2)*(Z^3) and put the number 2 into the Z variable, the graph of 8*(X^2) will appear when we press the GRAPH button.




Related questions




Q1. How do I graph a function of y?

Q2. When I try to graph I get error "dimension". What does this mean?

Q3. Can you give me some pointers on how to set up a good window to view a graph?

Q4. How do I find the intersection of curves when the graphs are done in parametric mode?

Q5. How can I plot the graphs of y=f(x), y=f ^-1(x), and y=x on the same set of axes?




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Basics of Calculator Operation
Functions
Limits
Derivatives
Curve Sketching
Integration
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Parametric Equations
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Vectors and Matrices
Functions of Several Variables
Multiple Integrals
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Problems Where the Calculator Gives an Incorrect Answer
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