A Turning Point Mystery (1 of 2: Introducing the problem)

[vasanthadevimanohararajah]

Mr. Woo,
Your videos are appreciated not only by students, even by teachers. I am 74 years old student using your videos to learn,
what I missed half century ago. I appreciate very much of this "turning point" video and your sincerity.!!!

[BrianAmedee]

If I am ever unsure how to teach/explain a specific topic in maths, I just watch HOW Eddie explains concepts. This is such a valuable resource to develop my skills as a teacher. Thank you Eddie 👍

[logi]

Hi Eddie your such an inspiration and help to people around Australia. You’ve helped me improved in maths so much in the past. And I know I’m not the only one.

[MathsCoach]

I really have been inspired by your work, Eddie. Its helped me a lot with my own content

[breandan]

The fun part is when you extend this function to negative x and the value becomes a spiral in 3-dimensional complex space. As x approaches 0 from the negative, the limit is also 1, or more properly (1, 0), but the it is discontinuous at x=0. In other words, looking at the transition from a 3-dimensional curve for x<0 and a 2-dimensional curve for x>0, it is not a smooth transition. Which is why x^x for x=0 is actually undefined, even though both sides approach the same value of (1, 0).

[elishaelisha]

I feel blessed to hear your class. Thank you

[mathonify]

This was a problem in the GCE exams last year. A very nice way to introduce it!

[marsch]

You are explaining so well. One of the best teachers. Waiting for part 2.

[dorset]

These are fantastic, Eddie.


Thank you.

[paulingersoll]

If you write the function as y = exp (xlogx) you can see that as x<1 the exponent is <0, so y < 1. Where xlogx is a minimum y is a minimum. This simplifies the minimum problem.

[redfeathersa]

This is a better video than the one of your lesson !! It's infact brilliant !! Very good!!! Very good 👍

[jkrifat]

it is the best way to teach...you should make video based on trigonometry....

[fgdtzoo]

Thank you for getting us through 3 unit!

[theguywhowouldnt]

Such an interesting lesson and such a great teacher.

[Samir-zbxk]

something funny about this function is if you take the sum of the two wrong answers you actually get the correct answer

if you incorrectly apply the power rule you get x * x^(x-1), and if you incorrectly apply the exponential rule get you x^x * ln(x)

the sum of these is x * x^(x-1) + x^x * ln(x) = x^x + x^x * ln(x) = x^x * [1 + ln(x)], which turns out is the correct answer to the derivative of x^x, which you can get by either rewriting x^x as e^[x*ln(x)] or by doing logarithmic implicit differentiation.

[arkammakra]

My god!!! Where’s part 2???😭😭😭😭 thank you so much for your very instructive videos M. Woo!

[Eric-reqi]

You can take the ln of both sides and implicit diff it right

[joaquinbadillogranillo]

This is a super good opportunity to use implicit differentiation!
We could also express x^x as e^ln(x^x) which is e^(x · ln(x)) but that's borring hahaha

[x-iy]

for this whole time i was waiting for part 2

[rnistuk]

A cliffhanger! DAMNIT!!! Fine! I'll solve it myself!