Prologue to Calculus (5 of 5: Gradient of the tangent)

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[@ariuwu1234]

I love how even though i had a basic understanding of the things, it really clicked while watching these episodes. Thank you :)

[@watchernotacritic8863]

I would do anything to have this guy as my professor. My current calculus professor doesn't teach or explain concepts like this. He just does equations with no explanation as if we are supposed to already know how to do it and naturally follow along. This series is amazing. I finally get it

[@EyeOnTheTV]

Looking forward to more on Calculus. Its a subject of math I've always considered beyond my comprehension throughout the days of my schooling and I never took it. It's finally clicking watching these .

[@yashkrishnatery9082]

This is how brilliantly a person can take you from bolt to calculus.... Really stand up for you Mr. Woo

[@mileswilliams527]

Always so well explained and simplified Eddie. Thank you for all your great work good sir. Much respect.

[@nalihnalih6443]

Whyyy am I watching this I finished high school and I don’t need that stuff anymore 🥴🥴🥴 it’s just interesting af and I’m am sad the maths in Highschool was pretty basic and low :/ hope university will be better ! Absolutely adore you!!!!

[@defco89]

What leap of logic did it take for ancient mathematicians to figure out that the function of a curve could itself be transformed into a more *_magical function,_* it's derivative... which could then, in turn, be *_used to find the slope of any tangent line along that curve._* This level of precision and intuition is something hard to grasp even in our advanced technological age. Your videos are a perfect way to connect with the elegant genius of the past.

[@huzefa1991]

Wow Eddie!! It was a wonderful series of 5 videos... Great way to start imparting elementary calculus education.

[@piggo5645]

Literally never touched calculus in my life and this was so easy to understand

[@Matt-sc6gg]

Exactly! That is the secret to effective learning: 1. be curious, stay curious- ask a curious question and have the grit to learn it and the growth mindset alongside! 2. learn complex things from educators like Eddie Woo and Tyler DeWitt who use simple language to explain complex things. even CALCULUS! 3. Practice more problems from The Organic Chemistry Tutor(Julio Gonzalez) and get a good grip over the subject. 4. Make sure you enjoy learning and don't stress out! 5. Don't study JUST to ace tests! Best of Luck!!! This strategy always works out for me! PS: I am in 9th grade!

[@marq6325]

@@Matt-sc6gg thanks alot

[@Matt-sc6gg]

@@marq6325 and listen to the Weeknd and chill af during breaks

[@marq6325]

@@Matt-sc6gg are you learning calculus in the ninth grade? Im amazed haha

[@Matt-sc6gg]

@@marq6325 I am not consistently learning I learned the absolute damn basics which is very easy, I can't solve very complex problems.... YET. PS: Now I'm in 10th Grade

[@adirtymoron]

THAT WAS THE COOLEST REVEAL OF ALL TIME!! "Look at what happens when you put in 2.. what does that mean?" Mr. Woo, you sir, are an absolute LEGEND.

[@ExileDriver]

Brilliancy!!! I must finish this playlist!!!

[@NunYaBiz404]

Man, calculus! It never ceases to amaze 🔥🙌

[@funkyflames7430]

amazing series! Looking forward to the tough stuff!

[@Onoma314]

This series has beautifully explained the fundamental Mesopotamian unit of the sar ( 3600 ) as well as the basis of their metrological systems ( Dimensional analysis ) Great teacher !

[@8dolev]

Amazing explanation. Too bad the bell cut it short right at the apex.

[@muhammedali8025]

surely he was cut short at the nadir ...x=2 y=-4

[@profenk]

The best teacher I’ll ever have

[@jinminetics599]

At 4:11, to get f(x), just do: x = 0 OR x = 4 //subtract the value of x from both sides x-0 = 0 OR x - 4 = 0 //multiply the LHS of both equations to get f(x) (x-0)(x-4) f(x) = x^2 - 4x

[@potatofmany]

tysm!

[@oogleeh]

That is really amazing. I used to hear about calculus, but I never saw the big picture. Thank you Mr. Eddie Woo.

[@bil9uun]

"Sometimes things get worse before they get better" - Eddie Woo

[@adityadalvi4483]

Just a quick question... How did he get the equation of the parabola as f(x)= x^2-4x? Can someone please help to explain?

[@jonoliahjohn6800]

Firstly, you can recognise that it is a parabola that extends to the positive region, so 'a' must be positive. You can tell that 'a' must be equal to plus or minus 1 because the graph is symmetric, going two units on either side of the central line. And since we know that 'a' is positive, the coefficient of x^2 is +1. Next, you can look at 'c' which is the y-intercept. The graph crosses the y-intercept at 0, so c is '0'. That leaves us with 'b'. The trick here is to imagine the graph centred at 0. At that point, a negative 'b' shifts the curve to the right while a positive 'b' shifts it left. And since there is no 'c' and 'a' is 1, the only way for the curve to cross at 4 on the right, is for 'b' to be -4. I really hope that helps.

[@anjaligarg8709]

We can also find it simply by observing that at x=0, y is also 0 and at x=4, y is again 0. This means 0 and 4 are the roots of that parabola's equation and since a parabola can't have more than 2 roots, we can obtain the equation of y=(x-0)(x-4)= x^2-4x

[@onejumpyboi2791]

Just saw him today at Oxely High School, he done some random card trick

[@robertbowen9750]

Holy shit dude. I think I might really like calculus.

[@andrewporter1868]

The way it's put there in the end implies that division by zero is nothing more than substituting a denominator of zero with an arbitrary variable and solving for the limit of that function as that variable approaches zero and defining that as the acceptable operation for division by zero. In other words, division by zero implies that dividing by zero returns an infinite set of solutions equal to f(x)/0 . This holds if we consider that f(x) * 0 = 0; therefore, all functions are valid coefficients of zero, so dividing a constant or a function by zero gives us a function that is a valid coefficient of zero, but since we are not working with expressions, but functions of x which map to y, then if we divide by zero for a given function, we must state that the result is the function that is both a valid coefficient of zero (which is redundant) and is also a valid multiplicative inverse of f(x) since division by zero is the inverse of multiplication by zero, yet since there is no real function which satisfies f(x)/0, there must necessarily exist a set of numbers where 0 != f(x) * 0, and not even the imaginary numbers are sufficient to describe it.

[@amarjot11a22]

Thank you sir you were very helpful student from india

[@nobitanobi2749]

I have a degree in accounting, and we talk about Tangible Assests before, and of course i knew it meant "assets that can be held" but i never knew it has something to do with the word TANGENT. 😂

[@tanushkakhanduja1057]

Calculus is beautiful!

[@frankbowman9493]

That was a great series of videos!

[@richardtrager7125]

Damn he kinda proved the process of differentiation

[@sebastianmarmorato]

math is beautiful

[@shakirafarooque3166]

I wonder how much detail you delv into

[@zebra2218]

Hi Eddie - Please Could you make Calculus in Physics Applications videos too if possible. Thanks,

[@avichal503]

Can someone please explain how she got the equation for the parabola using the two intercepts?

[@tomisoetan9061]

Thanks for another great video! Does anyone know how that student was able to know that the equation of the graph was x^2 -4x just by looking at it?

[@jakemcgregor14]

The roots of the graph were x=0 and x=4, therefore you can solve the quadratic already x(x-4). Only 2 years late lol

[@abhijeetrao7623]

Realy maths is a magic

[@practicecoach777]

What textbook are they doing their exercises homework from? Ta

[@asamoah-danquahstanislaw2002]

wooooow ,i really thought i had already learnt that .

[@koungmeng]

can't watch to learn integral with you xD

[@karim_ghibli]

2:15 I'm a mathematician and I'm offended.

[@the81kid]

Perhaps I missed another video with function notation(?), because I'm unclear how the limit (lim) equation and the curve equation (x²-4x) are combined. Can someone help me? or point me to a video showing me why it seems that each term from the (lim) equation is first plugged into the whole (x²-4x) equation, and then this new (x²-4x) equation is plugged back into the relavent term in the (lim) equation. This is confusing me!

[@rakib17874]

Yup. I'm confused too.

[@miguelfontenele221]

In the first video he teaches how to get the "difference quotient" equation which is [f(x+h) - f(x)]/h Them in other videos he explained that the smaller the hypotenuse of the gradient is them more precise your measurement is going to be so the idea is to see what happens if h gets closer and closer to 0 without actually being equal to 0 and that's why limits are related to that "difference quotient" equation. In this video he used the parabola "f(x) = x² - 4x" as an example, so if you plug that parabola identity in the equation i've put above you'll end up with 2x - 4. I hope that was clear enough, i don't have the talent of Mr Woo :D

[@musicfarhination2576]

And tank you

[@Aceo_0]

I should have known a few years ago

[@monoman4083]

is there a part 6?

[@musicfarhination2576]

Please sir please sir make a tradiction to arabic i'm from morocco

[@mapa5497]

Even I had proved in this manner only..

[@musicfarhination2576]

Sir please please please make a tradition to arabic because i'm from morocco and i'not good in englich please sir please sir

[@Flightless_stellars_jay]

The two dislikes are from Newton

[@sanrihoe3098]

2:43

[@msainmh2449]

HELllo

[@sebastianmarmorato]

1:33