f"(0) = 0, and around x=0, the graph is concaved upward, and x=0 is a critical point, so it's a minimum. Mathematically, i get how we got f"(0)=0, but isn't f"(0) supposed to be positive if it's a minimum (and not equal to 0)?
if a candidate for an inflection point IS a critical point, don't you already know that it can't be an inflection point, because critical points dont change concavity, and inflection points do
Some Random Fellow This is actually not true.It's possible for a number to be a zero of the first and second derivative and still be an inflection point. For example, there could be a horizontal tanget line there but it could change from concave up to concave down or vice versa(like the on the graphs of y=-x^3 and y=x^3 ).
don't worry! what you need is the foundation that you learn in both grade 10 and and grade 11 trust me this stuff get's MUCH easier once you have you're backgournd knowledge and you know you're algebra well lmao i don't mean to sound rude but it's not the best idea to jump from grade 10 to 12 you still have quite a bit to learn, why not try learning grade 11 math before going to grade 12 caclulus (which is the hardest math learned in grade 12)
I see now why calculus is so powerful.
The best differential graphing lesson ever - Sal you are a legend!
Do you have something against the quotient rule?
lmfao
Sal: Hairiness
5:02 That's one of the things that I like about Sal, he keeps it real !
Or he could've just used quotient rule
That was just amazing in the end!!
this is literally the coolest thing ever...
I had a final today THANK U SO MUCH!!!!
Thankyou sal! Your video makes the topic easier
the notation that came to mind is x = 3-dx instead of x
f"(0) = 0, and around x=0, the graph is concaved upward, and x=0 is a critical point, so it's a minimum. Mathematically, i get how we got f"(0)=0, but isn't f"(0) supposed to be positive if it's a minimum (and not equal to 0)?
at f''(x) = 0 the graph changes its concavity and f(x) is an inflection point. f''(x) = 0 can not tell you concavity.
@giulliabreis we're graphing the function, not the f '(x)
Hey! Can you make a video about Graphing a function polynomial over polynomial, something like x^2/(x-1)^2 ? Thank you very much! :)
(x^2) * (x-1)^-2
a = (x^2)
b = (x-1)^-2
a = 2x
b = -2 (x-1) ^ -3
2 * -2(x-1)^3 + ( -2 * -3 (x-1)^4 )
Well, it looks like the graph have a horisontal asymptote.. Should not you check if it is true or not ?
Hey why when taking the second D would you use the product rule and not the chain rule?
He used both product rule and chain rule, chain rule for the derivative of the second term, and product rule for the derivative of the two terms
khancavity
khan how if there are 2 variables? f(x,y)
@mysterman2 Hahaha it's not man, it's all baby steps, you get there eventually and it eventually just becomes concept rather than just memorizing
if a candidate for an inflection point IS a critical point, don't you already know that it can't be an inflection point, because critical points dont change concavity, and inflection points do
Some Random Fellow This is actually not true.It's possible for a number to be a zero of the first and second derivative and still be an inflection point. For example, there could be a horizontal tanget line there but it could change from concave up to concave down or vice versa(like the on the graphs of y=-x^3 and y=x^3 ).
KL JL lmao we just went over all this in calc now i get it
Why is the critical point x=+-3? how do you know when to do + and -?
Because x^2 = 9, and both -3^2 and 3^2 equal 9
where did natural log go during finding the first and second derivative?
Faiza Hanif, he found the derivative using the chain rule. Check out his chain rule video to know more about how it vanished.
I keep on thinking that at exactly the inflection point the graph just goes down:/
don't worry! what you need is the foundation that you learn in both grade 10 and and grade 11 trust me this stuff get's MUCH easier once you have you're backgournd knowledge and you know you're algebra well lmao i don't mean to sound rude but it's not the best idea to jump from grade 10 to 12 you still have quite a bit to learn, why not try learning grade 11 math before going to grade 12 caclulus (which is the hardest math learned in grade 12)
@dannyboy12357 Then i pray to you the mathmatical god to show me how to find the critical numbers of f(x)= 15xln(x)
finally, concavity...
if they are negative sloping beyond 3 and negative 3 why don't we see a zero point and an upside u shape tho?
if second derivative is less than zero it just means that graph is concave downwards, and what do you mean by zero point?
@mysterman2 you'll get there eventually
baby steps
@mysterman2 I do believe that is what she said.
厉害，这下做题好做了
九中理科实验班 对啊！
@mysterman2 I'm in the same boat as you!
🎉
@mysterman2 u might wanna rephrase that
@mysterman2 same here. I guess we just have to stick with it
You have a mistake in second derivate :D
2 times of 4Xon3
@@muhammedahmetovic4214nope
Yeah i give up......
I AM A MATHEMATICAL GOD
That's what she said...
Do you think you're better than Advanced Math Tutors. You're not. Sorry.
jealous?