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.
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 RU-vid who explain everything in simple terms for free.
@@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 RU-vid comments feel like time capsules. As if you look at people in their past state. Glad to read your positive outcome. Congrats!
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
@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.
***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.
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?
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.????!!!!
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'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?
