...Good day Newton, I've watched your presentation on critical numbers and have 2 comments for you: 1) Regarding the 1st function, in the Netherlands besides x = 3, we also include/consider the boundary numbers(x = 2 and 4) of the closed interval [2, 4] as critical numbers, to be able to determine whether these numbers are maxima or minima...2) Regarding the 2nd function I noticed an error at about time 7:36 at the beginning of the last cleaning up of the numerator where you write x^2 instead of - x^2 (it should be - x^2 - 8x + 9 = 0 - (x^2 +8x - 9) = 0 - (x + 9)(x - 1) = 0 resulting in the critical numbers: x = - 9 or x = 1 both in [-10, 10]), and we also include x = -10 and 10 as critical numbers in this case with a closed interval [-10, 10] because of the same reason as the previous case. Hope you're doing well... Thank you and take care, Jan-W
@@PrimeNewtons ...I'm all at your service Sir Newton (lol)... You're in good health, that's the most important thing in life, believe me Newton... Take care and good luck, Jan-W
@@PrimeNewtons The first problem was when you simplified the numerator of the derivative for the second problem, where you had an x^2 term and a -2x^2 term, which should combine to -x^2, but you ended up with +x^2. That should therefore result in a numerator of -x^2 - 8x + 9 = -1 (x^2 + 8x - 9) = -1 (x + 9) (x - 1). So the x = 8 critical number should have been x = -9 instead. The second problem was that your (incorrect) x^2 - 8x + 9 numerator doesn’t factor to (x - 8) (x - 1), which are actually the factors of x^2 - 9x + 8.
![CAMPปลิ้น | EP.82[1/2] แก๊ง 3 สาวเพื่อนซี้บุก CAMPปลิ้นครั้งนี้ห้ามเสียอาการ](http://i.ytimg.com/vi/_6WUjXHe1TM/mqdefault.jpg)
...Good day Newton, I've watched your presentation on critical numbers and have 2 comments for you: 1) Regarding the 1st function, in the Netherlands besides x = 3, we also include/consider the boundary numbers(x = 2 and 4) of the closed interval [2, 4] as critical numbers, to be able to determine whether these numbers are maxima or minima...2) Regarding the 2nd function I noticed an error at about time 7:36 at the beginning of the last cleaning up of the numerator where you write x^2 instead of - x^2 (it should be - x^2 - 8x + 9 = 0 - (x^2 +8x - 9) = 0 - (x + 9)(x - 1) = 0 resulting in the critical numbers: x = - 9 or x = 1 both in [-10, 10]), and we also include x = -10 and 10 as critical numbers in this case with a closed interval [-10, 10] because of the same reason as the previous case. Hope you're doing well... Thank you and take care, Jan-W
This past week was heavy. I appreciate your comments. I will have to redo some recent videos too. You are an angel, dear Jan-W.
@@PrimeNewtons ...I'm all at your service Sir Newton (lol)... You're in good health, that's the most important thing in life, believe me Newton... Take care and good luck, Jan-W
Thank you.
How have you been it’s been 3 years sense I’ve been in your class it me Thomas it’s okay if you don’t remember me but are you still at Lawrence
I remember you, Thomas. Hope you're doing well. I left during the pandemic.
There is something wrong in the second function thanks
Please tell me. It would be easier and faster to correct. Thanks.
@@PrimeNewtons The first problem was when you simplified the numerator of the derivative for the second problem, where you had an x^2 term and a -2x^2 term, which should combine to -x^2, but you ended up with +x^2. That should therefore result in a numerator of -x^2 - 8x + 9 = -1 (x^2 + 8x - 9) = -1 (x + 9) (x - 1). So the x = 8 critical number should have been x = -9 instead.
The second problem was that your (incorrect) x^2 - 8x + 9 numerator doesn’t factor to (x - 8) (x - 1), which are actually the factors of x^2 - 9x + 8.
I just saw that Jan-W came to the same conclusion for the first problem in the video for the second function. 😊