Here are the steps: 1) Find the 1st Derivative 2) Find the Critical numbers by setting the numerator of the f' = 0 3) To see if its undefined, plug denominator = 0 4) Go back and take f" 5) Plug in the Critical number in for f' & f", you see if you get a positive number out 6) If f" Positive Number = local minimum. f" is negative = local maximum 7) Done!
I honestly dont understand why i even go to class anymore. It is such a waste of my time! I go for 2 hours a day to calculus learning absolutely NOTHING, then i come home and watch this 11 min video it all makes sense! Thanks for the vids, you saved my life countless times :)
yes, i agree! i strive to point out minor mistakes using annotations, and simply delete vids that have more serious mistakes. the last thing i want to do is teach someone incorrectly or make a huge, confusing mistake!
thanks so much, none of my math professors and TAs can speak clear english and this is saving my life. Kinda getting mad at youtube for ads in the middle of the video. But keep up the great work
I know you've gotten this comment thousands of times but this literally just cleared up hours of lectures and frustration, brilliant channel thanks so much
I got three weeks to study for a calculus test. I didn't. Then I solved some question yesterday(It's 6 am here now) and realised I am way to shitty at it. Then came in your videos. Thanks a lot dude, Test scheduled at 10am.
This helps a lot. I already knew how to do everything but when my teacher introduced the more than or less than zero for the second derivative, he confused me completely. This video cleared everything up.
I like you calculating at this speed because if you go too fast, it is hard to keep up, whereas if you go at a steady speed, it is easier to comprehend. So keep up the good work bud! You aren't doing anything wrong
did this in leaving cert and forgot! now i am doing it in college! remembered in after the first min of the video! THNK YOU. you have helped to pass maths in College!
Thank you..... I have a test for tmrw, i was stuck in this problem Your.vids. has reallyyy helped in these derivatives,concavity, increasing ,.... Im really good at math,but i dont understand anything since we started calculus Thanks alot. :)
You still use the same logic just applying your knowledge of derivative of natural logs e's and etc. If you need help with doing derivative of those you should just brush up on that.
Wait I have a question. Thank you so much I understood everything, but what is the point of finding the second derivative to find the local max's and min's when you can just take the critical points you found, -2 & 2, and making a sign chart as you did in the previous video. That's what I did and still got the same answer.
The critical points of the second derivative are the possible point of inflection. The critical points of the first derivative are the possible local/absolute max or min. If the critical points (except VA) in the first derivative is substituted to second derivative and is greater 0 there is a local min at that point on the graph and vice versa.
Hi Patrick. Where you've differentiated f'(x) so f''(x) = (x^2+4)(-2x) - (4-x^2)2 x (x^2+4)2x where does the 2 outside (4-x^2) come from? I hope my question makes sense, thanks
@rr5001 Generally, calculus is split up into 3 classes, Calculus I, II, and III. Upper division courses might include differential equation and muli-variable calculus.
What happens if you are given a closed interval? For example, [-3,5]. If f''(-3) = negative and f''(5) = positive, is x = -3 a local max and x = 5 a local min? In my class, the interval can be included in the local/absolute min/max.
great video. heres a suggestion though, if you could put the steps in the description it would help a lot (i.e. step 1 find derivative, 2, critical numbers, 3 plug critical numbers in)..but great video!
@patrickJMT I have to say I agree... but only because I have a massive test in algebra, differenciation, matrices and integration tomorrow and I'd love some fast cramming videos... but good videos!
When you first found f' of the function, could it have been simplified further (from -(x^2+4)/(x^2+4)^2 by taking out the -1, and getting -1(x^2+4)/(x^2+4)(x^2+4), which would cancel out to -1/(X^2+4) as the first derivative? I got the same answers out of the problem when I did this, and it made finding the second derivative way easier... but I'm not sure if that's just a coincidence and I broke some major rule of algebra somewhere.
What's the point in plugging in the values for the critical point into the first derivative, if you're just going to find your local max/min through the second derivative test?
Isn't the quotient rule the derivative of the top multiplied by the bottom minus the derivative of the bottom multiplied by the top, over the bottom squared?
what if we do it the oda way arund by solving for second derivtive without findin the critical value of the first derivative. then at the end use a sign table to find both the relative max and min? nid ur urgent reply??? thanks
If I found my critical points, and then plugged in numbers to the left and right to see if the function is increasing or decreasing. For example if my function at a certain critical point was decreasing to increasing, Wouldn't I be able to tell whether I have a local max or min? So what's the point of the second derivative test?
What if the second derivative equals 2? my f(x) was x^2-6x, very simple but the second derivative ended up being 2 so I'm not sure how to determine concavity from that point.
He just flipped the sign of the equation to make it easier for him to solve it, but if u don't flip the signs u will get the same answer cause when u move the 4 to the other side it becomes -x^2 = -4 where the negative signs on both sides will cancel
Here are the steps:
1) Find the 1st Derivative
2) Find the Critical numbers by setting the numerator of the f' = 0
3) To see if its undefined, plug denominator = 0
4) Go back and take f"
5) Plug in the Critical number in for f' & f", you see if you get a positive number out
6) If f" Positive Number = local minimum. f" is negative = local maximum
7) Done!
forget little thing.. if its 0
@@al-maalaalmaawali260 if you put the c value in f"(x) and its 0 that means you found the turning point of the curve
You are the reason I am surviving calculus.
Thank you for this.
I honestly dont understand why i even go to class anymore. It is such a waste of my time! I go for 2 hours a day to calculus learning absolutely NOTHING, then i come home and watch this 11 min video it all makes sense! Thanks for the vids, you saved my life countless times :)
yes, i agree! i strive to point out minor mistakes using annotations, and simply delete vids that have more serious mistakes.
the last thing i want to do is teach someone incorrectly or make a huge, confusing mistake!
By far the best math teach iv found so far on youtube.
Better than Khan Academy.
+Asad Bilal thanks! Come back any time!
Khan academy is vague in calculus it's not that good. I prefer this channel or the organic chemistry tutor.
Brushing up for my calculus 1 final in 3 days. You are the reason why I'm passing this course
@L4ctose thanks for your useful comment. it is valued and appreciated!
YES. you have this videooo!! I slacked off after derivatives and was falling behind in class. This will catch me up :D
thanks so much, none of my math professors and TAs can speak clear english and this is saving my life. Kinda getting mad at youtube for ads in the middle of the video. But keep up the great work
In the first minute alone you helped me more than my professor
I know you've gotten this comment thousands of times but this literally just cleared up hours of lectures and frustration, brilliant channel thanks so much
You don't even know how much this helped me!!
Thank You!
you are welcome! :)
you are explaining better than my teacher. Thank you for this.
best math tutor on TH-cam so far, Thanks a bunch! :)
I got three weeks to study for a calculus test.
I didn't.
Then I solved some question yesterday(It's 6 am here now) and realised I am way to shitty at it.
Then came in your videos.
Thanks a lot dude, Test scheduled at 10am.
look just below the ratings (all the red stars) and to the right.
it is just below the 'run time' clock
patrickJMT, I am passing Calculus because of you. You are awsome. Thank you so much!
Patrick for president. Thanks heaps!
This helps a lot. I already knew how to do everything but when my teacher introduced the more than or less than zero for the second derivative, he confused me completely. This video cleared everything up.
I would say that most of your videos are perfect length. You usually describe to me perfectly what would take an entire lecture or two lol.
you are the only who saved me in calculus
my calc test grade will thank you tomorrow
thats crazy 5 years ago u were and calc and now im in calc
I like you calculating at this speed because if you go too fast, it is hard to keep up, whereas if you go at a steady speed, it is easier to comprehend. So keep up the good work bud! You aren't doing anything wrong
thanks to your channel i can officially not be worried when i go to class for a quiz or a test
:) thanks for this!!
did this in leaving cert and forgot! now i am doing it in college! remembered in after the first min of the video! THNK YOU. you have helped to pass maths in College!
you are a god, this example was the exact question i was trying to work out! love the videos, like a second teacher to me
Watched the first 1 min... gets the second derivative test ... ohhh thank you CALC GOD !
These videos saved my life. From a D in AP Calc BC to a B in 3 weeks. :D And now I'll be getting an A this quarter.
If I actually manage to get my degree after some years.... I will donate to you since u have helped me so damn much
Because of your videos I have passed math 3 .. thank you so much
Your videos are a life saver! I would probably be failing calculus without these videos.
Thank you.....
I have a test for tmrw,
i was stuck in this problem
Your.vids. has reallyyy helped in these derivatives,concavity, increasing ,....
Im really good at math,but i dont understand anything since we started calculus
Thanks alot. :)
@kevinr515 glad to help! thanks for letting me know about the ad in the middle - it should be gone now!
do you have any vids with really messed up examples? Like with e, ln, exponents and all that?
You still use the same logic just applying your knowledge of derivative of natural logs e's and etc. If you need help with doing derivative of those you should just brush up on that.
I definitely love your way of teaching it!! thanks a lot !!
You are the hero we dont deserve
@letthemxeatcake no problem, hope it helps.
this should be on trending every week #G.O.A.T.
hahaha, lovely singing voice!
i love your videos!! Im desperately trying to prepare for my math finals in 2 days! wish me luck :)
This is great, much simpler than having to do numerical analysis with the first derivative every time.
Thank you Patrick! :D My final is on this Wednesday and this particular video just unlocked the last closed door in my brain regarding the extrema.
great video, lost my notes and this really help. thanks.
Wait I have a question. Thank you so much I understood everything, but what is the point of finding the second derivative to find the local max's and min's when you can just take the critical points you found, -2 & 2, and making a sign chart as you did in the previous video. That's what I did and still got the same answer.
that is what a friend who i was perpetually in love with growing up used to always tell me : )
These are crazy helpful dude, thanks a lot!
You are an excellent resource. I hope by reviewing your videos, I will be able to pull up my grade in calculus. It's been 30 years since precalc.
The critical points of the second derivative are the possible point of inflection. The critical points of the first derivative are the possible local/absolute max or min. If the critical points (except VA) in the first derivative is substituted to second derivative and is greater 0 there is a local min at that point on the graph and vice versa.
@guitarsea003 optimization problems
@rpsc06 no phd
omg thank you so much for this video I'm doing calc homework right now and it is this exact same problem!
same here 😢
+bri farris same he.. not... LUCKY KIDS
Oh my, how did I forget this! Thank you again!
YOU SAVED MY LIFE.
THE LEGEND
i still do not mind hearing it ;) glad i could help you
You deserve 10M
Thank you so much! This really really helped me! I have a test tomorrow and I was so clueless. Thanks so much! :)
it would still work. since the second derivative is always positive, it would mean you have found a local minimum
Hi Patrick. Where you've differentiated f'(x) so f''(x) = (x^2+4)(-2x) - (4-x^2)2 x (x^2+4)2x where does the 2 outside (4-x^2) come from? I hope my question makes sense, thanks
THANK YOU THANK YOU THANK YOU! I need to study this for my exams!
@DJSt3v3n no problem!
Thanks dude....coming in clutch.
These videos have helped me so much, thank you!
@rr5001 Generally, calculus is split up into 3 classes, Calculus I, II, and III. Upper division courses might include differential equation and muli-variable calculus.
@richindiankid that sounds like a good idea. with a name like ' richindiankid ' i hope you gave a LOT! : )
Dude you're a life saver thank you so much
@LucLamontCaputo well, a math phd is not easy. and i do not want it. i dont want a uni prof job
What happens if you are given a closed interval? For example, [-3,5]. If f''(-3) = negative and f''(5) = positive, is x = -3 a local max and x = 5 a local min? In my class, the interval can be included in the local/absolute min/max.
You are a life saver
GOD you are such a lifesaver! Thank you so much
nice work, very easy to follow.
Why aren't you a university prof, your better than all my math profs combined!
thank you for this video sir ❤️
this has really helped me
great video. heres a suggestion though, if you could put the steps in the description it would help a lot (i.e. step 1 find derivative, 2, critical numbers, 3 plug critical numbers in)..but great video!
Once again, many thanks!
Do you plug your critical number solution of the second derivative into the original equation?
at 2:20 where 2x goes?
+Jayz Ortiz -x(2x)= -2x^2, he added that to x^2+4, and the result became -x^2-4 as it is shown at 2:20
@patrickJMT I have to say I agree... but only because I have a massive test in algebra, differenciation, matrices and integration tomorrow and I'd love some fast cramming videos... but good videos!
Very good explanation of a, sometimes, difficult method to understand ;)
@SamBM17 That's the derivative of the bottom of the second derivative (x^2+4)^"2" = "2"('x^2'+4)('2x'). The chain rule.
Thanks a lot for you useful video, Sir. It's been grat help. :)
When you first found f' of the function, could it have been simplified further (from -(x^2+4)/(x^2+4)^2 by taking out the -1, and getting -1(x^2+4)/(x^2+4)(x^2+4), which would cancel out to -1/(X^2+4) as the first derivative?
I got the same answers out of the problem when I did this, and it made finding the second derivative way easier... but I'm not sure if that's just a coincidence and I broke some major rule of algebra somewhere.
What's the point in plugging in the values for the critical point into the first derivative, if you're just going to find your local max/min through the second derivative test?
where did the +2 come from at 6:05
thank you sooo much this helped me so much..
nice one man, thanks for the clarification. awesome
thanks so much! it was great like always! :)
Thanks alot 🌹🌹🌹
It is useful
Strayed too far from Calc 3 and now I'm watching Calc 1 videos now.
Wish I could go back to the easier stuff.
Isn't the quotient rule the derivative of the top multiplied by the bottom minus the derivative of the bottom multiplied by the top, over the bottom squared?
Have a Calculas exam in an hour, after this I'm gonna make this test my bitch. Thanks a million!!! :)
what if we do it the oda way arund by solving for second derivtive without findin the critical value of the first derivative. then at the end use a sign table to find both the relative max and min? nid ur urgent reply??? thanks
@ 3:14 when you are finding the critical points, how is it possible to find those points without including the denominator?
I totally agree, you do have nice hands.
If I found my critical points, and then plugged in numbers to the left and right to see if the function is increasing or decreasing. For example if my function at a certain critical point was decreasing to increasing, Wouldn't I be able to tell whether I have a local max or min? So what's the point of the second derivative test?
@Eadaoin94 better to be 2 minutes too long instead of 2 minutes too short!
what if the denominator could be zero? Will that affect the other local min/maxes?
What if the second derivative equals 2? my f(x) was x^2-6x, very simple but the second derivative ended up being 2 so I'm not sure how to determine concavity from that point.
After -x^+4/(x^2+4) can anyone please tell me what he did to get x^2+4=0
at 2:52 ?!
He just flipped the sign of the equation to make it easier for him to solve it, but if u don't flip the signs u will get the same answer cause when u move the 4 to the other side it becomes -x^2 = -4 where the negative signs on both sides will cancel
Sarah Antar Thank you Sarah. I mean why he got the numerator -x^2+4=
Alharbi Abdulghani x^2-(2x^2) +(4)= -x^2+4
do you have videos wherein you apply maxima and minima to word problems? :)