I was listening to a discussion between two doctors and heard them say "there is a monotonic relationship between x and y" and something in my head brought me back to this video I watched my freshman year of high school, well over 8 years ago. I think this video is what brought me to understand that a lot of concepts in life are very simple, but people complicate them unnecessarily. This concept from this video and served me so incredibly well in life and taught me to know the "fancy" words, but also be able to explain them in simple terms. I hope to use that with my patients one day - thanks, Sal.
@@saraqostahterra4548 What a fun question! 11 years have passed and since then, I graduated high school, graduated college with a b.s. in neuroscience, took a gap year doing amazing stuff, then went to dental school, went to residency and now I am a dentist typing this. Thanks for the fun question! Hope this brings a smile as much as your question. :)
@@balligator Omg you actually replied haha. That's amazing man! These very old CZcams comments feel like time capsules. As if you look at people in their past state. Glad to read your positive outcome. Congrats!
It's times like these I can't believe I pay several thousand dollars to listen to a professor rant about one proof that barely makes sense and doesn't help with homework at all when I could look up very helpful, charismatic people on CZcams who explain everything in simple terms for free.
Hey Sal, graphing the derivative is confusing for most of us, I think is better if you do an example graphing the actual function, that way, it will be easier for most students to see how the slope changes on the intervals you are talking about
@muzic I might be 4 years late but it is because he was graphing the derivative the positive slope in the derivative is still a negative one in the original function
Nothing like confusing the crap out of me when he started graphing the derivative instead of the original function. triangkle gave me a clue. So even though the original function is decreasing from negative infinity to zero hence the neg 3 its derivative is increasing because the derivative is measuring the rate of change of the original function?
@sschinychin What is there to dislike about this video, the man gave up his free time to teach us something. Guys like him make me have hope for humanity again.
As someone else said, write it as z^4 times 1/4 and use the product rule. You get (4z^3 times 1/4) + (z^4 times 0). Then it simplifies to (4z^3)/4 which equals just z^3. And I don't recall him writing 3z in this video, just saying.
i'm confused...in the beg he says that if f' (x) > 0, then it's increasing and vice...here he had h' (-1) = -3, which is less than 0, yet when he starts graphing, he draws a positive slope. What am I missing here?
Also the slope of a u function x squared is also always increasing and it’s x axis is a straight line but just because the derivative is below the x axis doesn’t mean it’s slope is decreasing.????!!!!
***GRAPH IS DRAWN INCORRECTLY PLEASE READ FOR A BETTER UNDERSTANDING*** just so everybody understands correctly, the curves between negative infinity and zero and between 0 and 2 should look as if they can NOT catch water because our test has proven decreasing hence concave downward. the curve from 2 to positive infinity should look as if it CAN catch water because our test has proven increasing hence concave upward.
A few people who were born to be psychologists must have become mathematicians instead. Why? Because as my mom(who's a Dr. in Psychology)said "A joke about psychologists is that we take what everyone already understands and put it in terms no one does."
I was listening to a discussion between two doctors and heard them say "there is a monotonic relationship between x and y" and something in my head brought me back to this video I watched my freshman year of high school, well over 8 years ago. I think this video is what brought me to understand that a lot of concepts in life are very simple, but people complicate them unnecessarily. This concept from this video and served me so incredibly well in life and taught me to know the "fancy" words, but also be able to explain them in simple terms. I hope to use that with my patients one day - thanks, Sal.
i love hearing him talk.
"monotonicity.. monoto.. monotonicity! "
i love this man
If you get a notification after 11 years, please reply. And tell me, what are you doing now 11 years after your studies?
@@saraqostahterra4548
What a fun question! 11 years have passed and since then, I graduated high school, graduated college with a b.s. in neuroscience, took a gap year doing amazing stuff, then went to dental school, went to residency and now I am a dentist typing this. Thanks for the fun question! Hope this brings a smile as much as your question. :)
@@balligator Omg you actually replied haha. That's amazing man!
These very old CZcams comments feel like time capsules. As if you look at people in their past state.
Glad to read your positive outcome. Congrats!
samee xD he's like "mono... I can't even"
It's times like these I can't believe I pay several thousand dollars to listen to a professor rant about one proof that barely makes sense and doesn't help with homework at all when I could look up very helpful, charismatic people on CZcams who explain everything in simple terms for free.
Monotonicity, mono-i can't even write- monotonicity, MONOTO- MOONOTO monotonicity theorem...
Thanks a lot Khan academy
I love you man! you make it easy to understand this stuff! GBU (God bless you!)
It would be awesome, if these would be repeated in a more high-quality version.
Isn't it enough? Why do you need more?
true af @@novaastronomia8720
Hey Sal, graphing the derivative is confusing for most of us, I think is better if you do an example graphing the actual function, that way, it will be easier for most students to see how the slope changes on the intervals you are talking about
Elisandro Mena when you take physics 1, graphing derivatives are easy
Thank you for the simple explanation :)
Which values we will put in the functions to realize the increasing or decreasing?
so only when there is a variable in the denominator do u use the quotient rule (or product rule)??
@muzic I might be 4 years late but it is because he was graphing the derivative
the positive slope in the derivative is still a negative one in the original function
I love Khan Academy always so helpful.
such a difficult name for a simple concept
I am lucky to find this channel
is a constant sequence monotonic?like {3,3,3,3,3...3,...}
Yall have any more pixels?
So when x is lesser than 2 it would be all negative, because some portions are increasing when it is lesser than 0.
Thanks...
The slope at z=2 should be zero.
Nothing like confusing the crap out of me when he started graphing the derivative instead of the original function. triangkle gave me a clue. So even though the original function is decreasing from negative infinity to zero hence the neg 3 its derivative is increasing because the derivative is measuring the rate of change of the original function?
B Izzy yes
@sschinychin What is there to dislike about this video, the man gave up his free time to teach us something. Guys like him make me have hope for humanity again.
Math is fun!
Nice
Explanation
I think it is... it also determines minima and maxima. Monotonicity sounds a bit more ominous though
As someone else said, write it as z^4 times 1/4 and use the product rule. You get (4z^3 times 1/4) + (z^4 times 0). Then it simplifies to (4z^3)/4 which equals just z^3. And I don't recall him writing 3z in this video, just saying.
Are you still using youtube ??😁
That quotient rule tho 4:05
you know that your on the hard part of math, when the video only has 93.782 views...
YOU're also on the wrong path when it comes to English.
Or math
There are easy af
So called because it's monotonous?
i'm confused...in the beg he says that if f' (x) > 0, then it's increasing and vice...here he had h' (-1) = -3, which is less than 0, yet when he starts graphing, he draws a positive slope. What am I missing here?
I had the same question. he made a mistake.
Shouldn't the slope at x=-1 be going downwards? (Sal puts it upwards)
also
Shouldn't the slope at x=2 be flat? (Sal has it going upwards too)
he's not drawing f(x)=y. He's graphing the derivative of f(x)
Also the slope of a u function x squared is also always increasing and it’s x axis is a straight line but just because the derivative is below the x axis doesn’t mean it’s slope is decreasing.????!!!!
Wow i am visiting this 12yrs later
@itsme7221 totally agree with you on that, lucky for him though he uses a tablet, so it's just like writing with a pen on paper! :D
***GRAPH IS DRAWN INCORRECTLY PLEASE READ FOR A BETTER UNDERSTANDING*** just so everybody understands correctly, the curves between negative infinity and zero and between 0 and 2 should look as if they can NOT catch water because our test has proven decreasing hence concave downward. the curve from 2 to positive infinity should look as if it CAN catch water because our test has proven increasing hence concave upward.
Nice
Monotonicty theorm aswell, why does it need to be called anything, it's so simple; +'ve means increasing, -'ve means decreasing
A few people who were born to be psychologists must have become mathematicians instead. Why? Because as my mom(who's a Dr. in Psychology)said "A joke about psychologists is that we take what everyone already understands and put it in terms no one does."
isn't this the ....first derivative test..?
Mano-tonny-city function 😂😂
thats hard to write like that with a computer, the mouse goes evrywhere. i would go t\slow as fuck
It wasn't super clear what you meant by a function > 0.
I don't even know there is a name for this lol. I know all of this, but I have no idea it has a name lol
11 years ago!!!, i was onl 8 years old lol
YESSIR
the derivative of H (z) is not correct ...
It's not. It's correct.
You got the whole graph wrong...
It's rly hard to understand the problem because the graphics are so bad.
He is solving wrong