Find any x-intercepts and turning points for function.

Question

1. Use a graphing calculator to find any x-intercepts and turning points for the function f(x) = 2x³ - 13x² + 24x - 9.

Answer 1

To find turning points which are not either local minimums or maximums (that is, inflection points), a TI-84 will let you calculate and graph the numerical derivative of a function. Then use this function to find all its zeros. Those zeros which are not either local minimums nor maximums are the remaining turning points (inflection points).

If you would like the details, post a comment.

Answer 2

Sorry Jacob, I tried making a video for you, but it's hard to see my calculator screen. Let me try to explain on here.

I am using a Ti-84 plus calculator.

First thing is using the Y= button. For me it is just below the screen all the way to the left.

In the first line, enter the equation in the question.

The function you want to use is the "CALC" function. It is the secondary function of the button on the same row.

That function will show the zero, minimum, and maximum among other things. The zero will tell us the x intercepts, and the max/min will tell us the turning points.

Let's start with the zero. It should be option 2. On the bottom left of your screen it will say "left bound". Move your cursor to the left of any point of the graph that looks like it intercepts the x axis. Try to get as close as you can. Then hit enter.

Now it will say right bound. Do the same, but to the right.

Now it will say guess. Hit enter. It will probably say 2.99999999 or 0.5 depending on which intercept you started with.

For the max or min, go back to the CACL function, do max or min, and repeat the same process. If you're doing max, you want to get to the left and then right of where the graph peaks (x=1.333).

For the min, do the same process around where the valley is (x=2.99999999).

Let me know if that helps or if you have any questions! I'll try to make another video if this isn't clear enough.