Inflection point intuition

[cinematics321]

haha At Math486 anyway, thank you Sal for all your math help

[fulouzero]

Thanks for the video man, this is just what I needed for the final tomorrow.

[maths486]

@ marcriganoskate :

There are lots of functions where the derivative at an inflection pt. is NOT 0. Let's take f(x) = x^3 - x

f ' (x) = 3x^2 - 1

f '' (x ) = 6x

Now 0 is an inflection pt. ( Not simply because

f '' (0) = 0 ) but BECAUSE f '' (x) will change from negative to positive at 0. So 0 is an inflection pt., and also f ' (0) = - 1 ( meaning the tangent line at 0 (the inflection pt ) is NOT horizontal )

I hope this will clarify things for those who got confused by this video.

[ichinarukurumaki]

yea you dont have to be an asshole

[maths486]

I have to correct what this guy from Khan Academy said. He said if the first derivative at a number is 0, and so is the second derivative, then we have an inflection pt. at that number.

This is obviously wrong and gives students a wrong intuition.

Take the simplest f(x) = x^4 f '' (0) = 0. But 0

is definitely NOT an inflection pt.

[Calc450]

i do understand your point, and i do agree with what you said for the most part. However, i do not agree with your presentation.

"I have to correct what this guy from Khan Academy said."

Clearly you have lost any sense of manners you have. Salman Khan is a professor teaching many subjects for reasons that are very kind and charitable. You have no right to address him as "this guy." if you do not speak to your colleagues or teachers like that, then do not began with sheer impudence.

[Calc450]

maths486 was to whom i was responding, as i forgot mention in my previous reply

Quite disrespectful, maths486.

[timmytankTK]

@maths486 All he said was is f '(x) = 0, then it was a point of interest. (max,min,inflection). He never said that only those points could be inflection points. He didn't even say they had to be inflection points. Watch the video twice before you make an ass of yourself.

[fromnyny]

Thanks so much for all your work!!! you're an amazing teacher!!

[shansra11]

Really great videos, but the derivative at inflection points is not always 0. To find inflection points, you find the critical points of the second derivative

[marcriganoskate]

do you know of an example where the derivative of an inflection point is not zero?

i always thought that the curvature changes at an inflection point and so it MUST be zero at the precise point of change.

[equalitykills]

helped me for calc ty

[tomiczkos]

it is very useful that people post such films, but I had to wait whole 6 min to get to the point. a bit too chaotic i might say

cheers

[BigPurple121]

WTF this video isn't loading

[mrmagic112233]

its a tragedy that after taking 8 months of calculus, our highschool class realized that they were not even remotely prepared for the AP exam, primarily because the meaning of our math was never understood. We did , what we were told to do and preety much admonished for questioning any principle we wanted to deeply understand. Thankfully, we have the internet, and videos like these to bring us back to speed.

[montelka]

for example f(x)=x-3x^1/3

[montelka]

how do you tell the inflection point without creating the signs, what aboout when the f"x is not zero or cannot be calculated.

[jachina]

Thank you for the video, i'm taking calculus, so this helps me alot

[wickedcool4yes]

Thanks, all your videos help so much in pelim HSC.

[its123baby]

Just a correction to a comment made at the end of this video.

if f'(x)=0 and f''(x)=0

this does NOT imply this is an inflection point. There must be a sign change in order for there to be an inflection point, and without more information no conclusion can be made.

This is according to the 2nd Derivative Test and was actually a question on my test for Calculus class.

Anyhow, keep up the great work Sal!

[its123baby]

*Important Note*

I'm pretty sure this only applies according to the 2nd Derivative Test.. Hopefully your teacher isn't a super technical professor like mine and won't even bother with this stupid rule

[khanacademy]

You are correct. If f'(x)=0 and f''(x)=0 at some point C that is not an inflection point, then you are dealing with a horizontal line (the slope isn't changing). I should have pointed out that exception.

[juaneco1980]

Oh, I was just about to ask that. But yea you should probably add that as a comment on your video. Anyway, thanks a lot for your videos you're doing an awesome job.

[khanacademy]

We could say that we are definitely at an inflection point if f ''(x)=0 at a point and f '''(x) does not equal zero at that point (implying a sign change in the second derivative)

[darkfighte]

awesome! now im prepared for ap calc bc next year.. By the way..You shud do calc 2 as well.

[ajwchin]

I'm doing BC also, going to be awesome.

[AkashP4]

The way you explain it makes it look so simple. You are ten folds better then my current professor. I say we fire all the current professors and watch your videos instead. Thank you a million times!!