00:01
All right, we want to find the points of inflection, which means we're going to have to take the second derivative.
00:06
Okay, i'm telling you, i've worked this problem several times, and the best way is to go ahead and multiply it out at the beginning so that we don't have to use the product rule.
00:16
Okay, so we get one minus x plus one -fourth x squared, x to the fifth, minus x to the sixth, plus one -fourth, x to the seventh.
00:31
Okay, so the first derivative is, okay, sorry, it's not taking the derivative with the product rule that's hard.
00:39
It's the simplifying.
00:40
Okay.
00:42
So 5x to the fourth minus 6x to the fifth plus 7 fourths x to the sixth.
00:50
And then the second derivative, 20x cubed minus 30x to the fourth plus 42 fourth, which is 21 halves, x to the fifth.
01:04
We want to find out where that's zero.
01:09
So factor out an x cubed, and you get 20 minus 30x squared.
01:16
Oops, 30x plus 21 halves, x squared.
01:26
So x is zero, or, all right, i don't know how to factor it.
01:31
I'm just going to use the quadratic formula on it.
01:33
It's minus b plus or minus b squared, minus 4a, c all over 2a.
01:49
So 30 plus or minus 900 minus.
01:56
This two cancels in there.
01:58
So that gives me 40 times 21.
02:01
So 840.
02:07
So 30 plus or minus the square root of 60 over 21.
02:14
60 is 4 times 15.
02:17
So 30.
02:19
That's not going to help us.
02:20
Let's just do it like this.
02:23
All right.
02:23
So we've got to get us some decimal values here so we'll know about where this is.
02:31
Okay.
02:34
If i'm a calculator, okay, square root of 60 plus 30 divided by 21.
02:46
Okay, so with the positive in there, we get one, let's just say 1 .8.
02:57
I'm having some trouble with my wire there.
02:59
Okay it's about 1 .8 for one of them okay oh i forgot to turn the pin back on okay equals 1 .8 and then the other one square to 60 negative plus 30 divided by 21 i'm going to say 1 .1 for that one.
03:47
All right so we got zero 1 .1 1 .8 and we're checking the second derivative.
03:55
Second derivative, which is x cubed and then 20 minus 30x plus 21 halves x squared.
04:10
All right, pick a number bigger than 1 .8...