But let's see if there any other inflection points, or potential inflection points.

These are both inflection points.

So these definitely are inflection points.

Let's see if positive and negative 3 are inflection points.

They might be maximum points, they might be minimum points, they might be inflection points, we don't know.

And let's see if we can find any candidate inflection points.

So let's see if there any other potential inflection points here.

And remember, candidate inflection points are where the second derivative equals 0.

Well, I've been requested to do some videos on concativity and maxima and minimum points and inflection points, and all the

And in the next video, I'll give you a little intuition on what happens with inflection points.

Now if the second derivative equals 0, that doesn't tell us that those are definitely inflection points.

So I think we're ready to plot. so first of all, is x plus or minus 3 inflection points?

But anyway, I will do the next video on inflection points, and then I'll do a bunch of actual problems.

So what we have to do now, is to see whether the second derivative changes signs around these points in order to be able to label them inflection points.

And then we know that the points positive 3 and minus 3 are inflection points, and in order to figure out their y coordinates, we can just evaluate them.

So hopefully you appreciate the usefulness of inflection points, and second derivative, and first derivative, in graphing some of these functions.

Let's see if we can use everything we know about differentiation and concativity, and maximum and minimum points, and inflection points, to actually graph a function without using a graphing calculator.

It's an inflection point.

But hopefully, you at least have an intuitive sense of what inflection points look like and what the second derivative is telling us.

Then, you know, once you do all the inflection points and the max and the minimum, you are ready to graph the function.

We have an inflection point.

It's a potential inflection point.

Well, what's an inflection point?

So these are our candidate inflection points, x is equal to 0, x is equal to plus 3, or x is equal to minus 3.

It's just a curve without inflection.

So this is an inflection point.

Normal IQ distributions have a stipulated average value of 100 IQ points and a standard deviation of about 15 IQ points.

But we are at an inflection point.

So 0 is not an inflection point.

So this is also an inflection point.

Maybe it goes to an inflection point.

So 0 is definitely not an inflection point.

But y can take on any value, so at points it's going to be irrational.

And these are the inflection points that tell you what the next chapter in that technology's life is going to be, and maybe how you can do something about it.

We figured out that this was an inflection point.

It's because you're all doing a cross model synesthetic abstraction, meaning you're saying that that sharp inflection ki ki, in your auditory cortex, the hair cells being excited Kiki, mimics the visual inflection, sudden inflection of that jagged shape.

It's because you're all doing a cross model synesthetic abstraction, meaning you're saying that that sharp inflection ki ki, in your auditory cortex, the hair cells being excited Kiki, mimics the visual inflection, sudden inflection of that jagged shape.

For example, if the true value is 50 percentage points, and the statistic has a confidence interval radius of 5 percentage points, then we say the margin of error is 5 percentage points.

And now we can solve for when the first and the second derivatives equal 0, and we'll have our candidate, well, we'll know our critical points, and then we'll have our candidate inflection points, and see if we can make any headway from there.

Has the eurozone, at long last, reached the inflection point?

We already know that this is a potential inflection point.

And it says prove that this has no inflection point.

After all that work, we were able to use our calculus skills, and our knowledge of inflection points, and concativity, and transitions in concativity, to actually graph this fairly hairy looking graph.

The maximum absolute value acceleration peak shall be recorded for each of the specified frequency break points.

But we figured out that this was an inflection point, right?