Ok, this graph is on inflection points, or inflection point of a graph, and let’s get
started – you put index8 in here, ya know, second alpha for the letters and then
Alpha eight, closed parenthesis, and that’s the code for my menu to come up, and here’s
the menu, of all different things that I’ve programmed so far, so we want inflection point
– so we’re going to scroll down here, there all in alphabetical order, so were going
to scroll down to inflection point there – press enter – and you can see that this is graphing
by hand, you have concavity, critical points, crosses the x and y axis, inflection point,
intervals of increase and decrease, and local maximum and mins. All these come up in my
graphing by hand program that I have designed. And so, I tell you to, ya know, mark of course
on your graph paper or test this, ya know graphing, ah axis, and then we’re going
to enter the function, so – you have to press alpha first – let’s enter minus
x cubed plus three times x squared minus two, press enter twice, it shows you what you’ve
entered – you can go back and change it if you want, I say it’s ok and I’m going
to press number one, and you can get all these from that function, you can get all of these
uhm different answers, so we want inflection point number six, I’m going to press number
six and uhm, notice the way you do the inflection point, you take the first derivative and then
you take the second derivative, here’s the six times x times x squared the first derivative
and then the second is six minus six times x, and then we’re going to factor it, factor
the second derivative and you get minus six times x minus one equals zero, so x equals
one – x component of inflection point – and you plug that into the original function – I
show you how to do that here – here’s y – the original function – and we’re
going to put one in for x – here’s x cubed plus and plus one into three x squared, and
when you compute that out it comes to zero – so the inflection point is really one
and zero – x equals one and y equals zero – mark this on your pencil graph and label it, ya know, pretty neat huh, check
my web site out – everystepcalculus dot com.
