00:02
So for this problem we're given the function f prime of x equals x squared times x minus one over x plus six until the x can't equal negative six and for part a we want to find what the critical points are of f our original function.
00:18
So critical points and critical points happen at places essentially where something interesting is going on.
00:26
So where either our first derivative is equal to zero or where it's undefined.
00:32
So we already know that negative six is a place where it's undefined on the bottom.
00:38
That's not actually part of our domain here but it is something that we're going to have to consider when we look at our sine line here in a minute to find increasing and decreasing and maximum.
00:48
And then where it's equal to zero we just want to take the top of the fraction and set that equal to zero.
00:53
So x squared times x minus one equals zero.
00:57
We split these up that's going to give us x equals zero and x equals one.
01:04
So zero and one are critical points.
01:06
For part b we want intervals of increasing and decreasing and so for that we want to make a sine line using the critical numbers we just found.
01:18
So f prime we want negative six zero and one.
01:24
And so i know already negative six is undefined and it's the bottom of a rational function so this is going to end up being a vertical asymptote...