 Hello and welcome to the screencast today about finding critical values of a function. So remember the definition of a critical value says it's any point C such that f prime of C is zero or f prime of C is undefined. Okay and just so you know for a lot of our videos we're pretty much going to be focusing on the first one and that's because typically the second one only happens if you have a corner or a cusp or maybe an asymptote from a rational function or something but you always want to remember to check this condition. It's just most of the time that's not going to apply for our problems that we're going to be doing. Alright so today we want to find the critical values of the function y equals x squared minus 1 quantity cubed. Alright first thing we need to do is find the derivative so dy dx is going to equal. Well we've got to dig back into the toolbox how do we do the derivative of this function and I see an inside function and an outside function so that means I'm going to want to use the chain rule. Alright so the chain rule says go ahead and bring down that power, rewrite your inside function, reduce your power by one and then multiply by the derivative of the inside. Okay so now that we've got our derivative now our job is going to be to figure out what values will make this derivative zero or what values will make this derivative undefined. But as I already said before this is a polynomial so it's not going to have anything that's undefined with this one. So basically we need to figure out where this derivative is going to be zero at. Well if you remember kind of how algebra works there are a few different ways we can attack this. I look at this and I see basically three different pieces so I see the piece of three but that can never be zero so we can ignore that. I also see this piece of x squared minus 1 we happen to be squaring it but that's not really going to change anything and then I also see this piece of 2x. So what we're going to do then is we're going to take each of these pieces and set them equal to zero. So if we take x squared minus 1 and set it equal to zero and then take 2x and set it equal to zero. So here obviously x is going to be zero divide both sides by two. Now this one over here you can add the one to both sides and take the square root but I bet you're going to forget one of the answers. So with this one I think it's a lot better to factor. So x squared minus 1 factors is x minus 1 and x plus 1 so that way now I can set each of those factors equal to zero and I end up with all my critical values. So I get a critical value of 1, a critical value of negative 1 and a critical value of zero. So these are all of my possible critical values for this particular function. Thank you for watching.