Patrick, I have to thank you for the clear math tutorial you are offering online via youtube. I am a student in one of the colleges in Ontario, Canada and just enjoy watching your math and calculus problems with your fascinating explanation. So clear, that I get it right after watching one or two times about a problem I have! I thank you for everything you do to your community and others by taking time, video recording these math problem solving. Sam
Haven't gone to math class the entire unit. Test tomorrow at 10:30, haven't learned a thing due to my laziness. However, thanks to aderol, an all nighter, and patrickJMT, I may be able to ace this fucker. You're a fuckin' bro JMT, a fuckin' bro.
zjuan8 lol yeah me too, after I posted that comment, I was like, "Wait, I need to know this for finals, don't I.." The past always comes back to haunt you, I swear -__-
Thank you! I've been looking at Khan Academy because all the comments say it's so great and was staring at his videos like an idiot. You clear everything up!
+Kevin Carrasco Hahahaha I second this. I'll even throw a speech for you when I do my walk to pick up my diploma. "I could not have done without w/o +PatrickJMT"
i'm studying for my EIT (engineer in training) exam, saw your video on the side and the memories came rushing back. made me happy. I had to stop by and show some love.
The fire alarm was going off in the background but Patrick disregarded it and put his life on the line in order to save math kids around the world from failing. A real hero . :)
You are a lifesaver! I am currently enrolled in an online calculus class and there is NO lecture. I just can't get these concepts without seeing and hearing someone explain it. I've lots watched of videos, and yours are some of the best. I'm telling the rest of my class about you. :)
I loved PatrickJMT when I was taking calc four years ago and I still love him today as I am tutoring and he makes great refreshers. Thank you PatrickJMT!
Yes, you are correct with everything you did in that 2nd problem you did. 1 divided by the square root of 5 is about .447 or .45 depending on how you want to round it up. Between the numbers 1 and the fraction problem with the square root sign, no matter what number between those numbers you plug back into the 2nd derivative is going to be negative either way. And you know, what else is unique about this problem is that this problem is showing that the concavity keeps flipping up and down. It's very wavy when you graph it.
I just wanted to thank you so very much for the amazingly easy to understand videos which you have posted all throughout RU-vid. I got a 97 in calc b/c of you PatrickJMT!! Keep it up! :)
Just wanted to say-- My math department steals problems from MIT, and this is the exact first example they had me doing in my homework. No coincidence- you're a great teacher!
once you have it factored, you set each part equal to zero. since 6 can not equal zero, we just leave it out. and for the factoring part: i use the difference of perfect squares formula: x^2 - y^2 = (x + y)(x - y) so to factor x^2-1, use x^2 - 1= (x + 1)(x - 1) and the same thing on the 5x^2-1 part!
makes me so happy when i understand this stuff! ahah. i use your vids every day for calc & feel like i should thank you in every vid i use! so thanks :)
Dear Patrick, Thank you so much for uploading all of these videos! I know this is bad, but I occasionally I fall asleep in my AP Calculus AB class and miss parts of the lesson. Your videos are PERFECT for filling in my mental holes. I really think RU-vid should give you an award or something for your contributions. :) PS i love your handwriting.
Patrick, you rule!! Wish I could replace my Calc I teacher for you instead. You get way more done way faster and explain so much better. Probably gonna be destined to re-taking Calc, but you've "got my back" so to speak.
My calculus book...is terrible at giving clear examples (Some are good but are either too easy or are exceptions to the normal problems)...so thank you very much for your examples. Makes the whole process a lot easier. I can't imagine how many test scores you have single handedly improved solely because of these videos.
first one was critical points , which is used to check whether the function is decreasing or increasing and this one is inflection point .Inflection point is where the concavity of f(x) changes (goes from conave up to concave down, vice versa).
Here is my day... Go to calculus class and become confused. Go home and get on this channel Find exactly what my teacher was trying to explain on said channel Finally understand!!!
You have to plot the values 1, -1, 1/sqrt5 and -1/sqrt5 on a number line like he did and then you have to test the numbers around these plotted points. So you have to find a # left and right of the plotted values and then plug them back into the 2nd derivative to see if you get a positive or a negative answer. If you get a positive answer then that means you have a concave up and a negative answer means concave down.
The 2nd derivative is just the derivative of the 1st derivative. Ex: F(x) = X^2 + 3x 1st derivative: F'(x) = 2x + 3 2nd derivative: F''(x) = 2 Hope that helps!
I thought it was hilarious how I could hear a saw and a car horn going off at the same time in the background. I don't know why I found it funny. I have an exam next week and a final in 6 weeks, thank you Patrick.
I was confusing whether to put critical numbers from f" back into it when I should have been putting in numbers more or less from the crit numbers. THANKS BUNCHES!
What is the difference if you look at the critical numbers of the second derivative vs the first? In the previous lectures you look at the critical numbers on the first derivative, but here on the second. Have exam tomorrow, fast answer is appreciated!
Inside the brackets he had [(x^2-1) + 4x^2)]. You can simplify this. Its the same as [1x^2 - 1 + 4x^2]. So you have one x^2 and four x^2. If you add that together you get 5x^2 and a minus 1.
Because what you found are the inflection point, after you graphed them, and found the concave up in the numbers bigger then one, you already know that before 1 it's concave down, and before that concave up, and so on, you didn't have to found each point separately.
