And then we know at x is equal to 0, we also figured out that the slope is equal to 0.

So we can write, f prime of 0 is equal to 0.

Or 1, 0, and then 0, 1.

And actually your teacher might want you to plot these points, and there you just substitute y equals 0.

Either x minus 3 is equal to 0 or x plus 2 is equal to 0.

And then what is f of 0, just so we know, because we want to graph that point? f of 0.

You can say 100 times 0, minus 3, times 0.

But m could be 0 as 0 can be expressed as 0 1 or 0 2 or 0 3 or 0 537 these are all representations of 0

So let's set that equal to 0, and then solve this problem right there.

Five seven three two with a zero behind it.

4 times something to the third is equal to 0, that something has to be 0. x to the third has to be 0, x has to be 0.

Well, the numerator can be equal to 0 because this thing can equal 0.

So now we can say that x plus two equals zero, and x plus four is equal to zero.

And the reason why even though this is completely not intuitive, and you could type in 0 to the zeroth power in

We know that f of 0 is 0, right?

If we wanted to set this equal to 0, we just say 4x to the third is equal to 0, and we know what x value will make that equal to 0, x has to be equal to 0.

Which either means that x minus 3 equals 0 or x plus 2 equals 0.

I mean, you could say x minus 7 is 0 or x minus 7 is 0.

Maybe this is 0.

You bring down this 0.

It could be 0.

So they have to be equal to 0.

You could view this as plus 0.

And you say OK, this has to be equal to 0, or that has to be equal to 0.

We know that the second derivative is 0 at 0.

You can always multiply A times 0 to get 0.

They also tell us that at f of 3 is equal to 0.

And then 4 minus 4 is 0.

And then, I have a 0 here.

You could say, x2 is equal to 0 plus 1 times x2 plus 0 times x4. x2 is just equal to x2.

So x can be equal to 0 so 0 plus or minus 2.

And obviously, as x approaches 0 of x, that's also going to be 0.

And we could draw a couple of examples. f of 0, well we go to 0 on the x axis, and we say f of 0 is equal to 0. f of 1 is equal to well, we go to x equal to 1, and we just see where the chart is, well, it equals negative 1.

So this thing is going to be equal to 0, either if 12 x is equal to 0, so 12 x is equal to zero, that gives us x is equal to zero.

This could be equal to 0.

It can't be equal to 0.

We want to solve for x equals 0.

We want these to be 0's.

We know that the slope is 0.

It's just that the slope is 0.

And sure enough that equals zero.

Right, the derivative of a constant is 0.

So we can bring down a zero over here.

Or x minus 6 is equal to 0.

So this has to equal 0.