It's crazy that this video was uploaded almost fifteen *years* ago. Thanks for your continued commitment to assisting those who struggle with these concepts!
i am a senior in high school now in my final weeks before graduation. Thank you so much Mr. Khan for all you have done for me over the last few years of high school. Your videos have helped me better understand so many concepts in math, and I'm sure it has helped many, many others as well. thank you so much.
Thank you so much!!! My calc teacher is currently going on paternity leave so I've been completely confused but optimization is making more sense to me now!!
***** damn, I have a final in three days and my problem areas are in related rates and optimization as well. Just wanted to ask for reassurance in a way lol. Do you think you passed the class?
Another test you can do is a sign test using the first derivative. You find all critical points at which the derivative is equal to zero, and you look at the signs left and right of the critical number. If the function of the first derivative goes from positive to negative at a critical point, it's a relative maximum (could be absolute if it strictly increases prior and decreases strictly after). If it goes from negative to positive, it's either a relative or absolute minimum.
256 IS a function! It is a constant function represented graphically by a horizontal line. Since there exists one and only one y value (256) for every x (all real numbers) f(x)=256 satisfies the criteria of mapping from domain to range in a function!
@username15219 you can... but it will probably take longer, i always use the 2nd derivative in case you are asked to find inflection points and so forth
This helped me understand a basic idea of solving optimizations, so I thank you. Though would this same method be used when we take real world examples, such as finding the max volume of a box?
out of his quick jokes - this has gotta take the cake 'save my electronic ink' - lmao!!!!!!! well apart from the infamous '(s)e^x, i sometimes think about this when i go to bed' - sal, keep up the good work, u share the unselfishness of the late nikola tesla and humorous side of einstein... thanks heaps... save my electronic ink, loool.....
No. Once you solve the derivative for x and get y, (at around 6:22) you are done with the problem. The rest is just checking to see you did-nt make a mistake.
A company makes and sells X digital cameras/week. the weekly price-demand and cost equations are, P=400-.04X; C(x)=2000+160x. (a) What price should a company charge for cameras, and how many cameras should be produced to maximize weekly income? (b) what is the maximum revenue? Can you please solve this word problem? One i see it solved i can figure out the pattern and apply it to the other similar ones i have :-) Thanks
Well Sal, i understand that you have a 10 minute capacity but that's actually the cap before you're allowed to enable advertisements on your videos. It would be good to profit yourself as well as others by teaching and making ad revenue.
![How to Solve ANY Optimization Problem [Calc 1]](http://i.ytimg.com/vi/cUMvwG7wvzM/mqdefault.jpg)
Mr. Khan, do you realize that your videos saved numerous lives?
6rosebudX probably literally as well
Dude is practically Jesus
Preach. Literally watching this through my tears
too bad he killed some pixels
Khan if i had a penny for every teacher that taught like you, i'd have a penny.
And, thanks to everything you can learn on Khan academy, you'd know exactly what to do with that penny to change the world.
Dude that was very well put!
And a penny is all you would ever need
Wow
I have a final in an hour and a half so might as well learn now
literally me rn
Accurate
Yep
big mood
I feel you bro
It's crazy that this video was uploaded almost fifteen *years* ago. Thanks for your continued commitment to assisting those who struggle with these concepts!
i am a senior in high school now in my final weeks before graduation. Thank you so much Mr. Khan for all you have done for me over the last few years of high school. Your videos have helped me better understand so many concepts in math, and I'm sure it has helped many, many others as well. thank you so much.
I just wanted to thank you for simplifying the idea of optimization! I just might ace my Calc test tomorrow due to you! ^.^
Scarletontherocks11 ace your test means guess every problem and hope right
Did u pull it off?
this video is from exactly 12 years ago. Still relevant and saved me a bunch of struggling.
Once again I thank you Sal. This really cleared up my confusion, since my teacher only uses the easy examples and gives us harder problems for HW
Yo bro, I’m very curious what do you do for a living?
@@josephcook8972 you really think he is going to reply?
@@sufyansiddiqui7624 do you really think HE is going to reply?
Thank you so much!!! My calc teacher is currently going on paternity leave so I've been completely confused but optimization is making more sense to me now!!
Thumbs up if you're watching in 2050
OMG, more than 60 people came from the futur
Does 2020 count?
I'm watching in 1492.
I have a gay ass test tomorrow and this probably saved my ass thx
+AsianMLC same here lol
+AsianMLC i have a final exam too tomorrow :/
+AsianMLC i have a lame ass semester final tomorrow
+Lester B How was it?
***** damn, I have a final in three days and my problem areas are in related rates and optimization as well. Just wanted to ask for reassurance in a way lol. Do you think you passed the class?
“Save my electronic ink” 😂
I swear.. Khan Academy has saved my life. x.x
I would just like to take a moment recognize the amazing "y^2" at 1:30
Very helpful stuff for the machine learning students
Another test you can do is a sign test using the first derivative. You find all critical points at which the derivative is equal to zero, and you look at the signs left and right of the critical number. If the function of the first derivative goes from positive to negative at a critical point, it's a relative maximum (could be absolute if it strictly increases prior and decreases strictly after). If it goes from negative to positive, it's either a relative or absolute minimum.
yes
I was sick during the optimization unit, my test is in two days, and my final is in a week. Bless you.
You're wonderful. I can't even tell you how much these videos have helped out.
Calc exam tommorow, chilling around watching ur vids
256 IS a function! It is a constant function represented graphically by a horizontal line. Since there exists one and only one y value (256) for every x (all real numbers) f(x)=256 satisfies the criteria of mapping from domain to range in a function!
I always graph these once I find the equation, it helps me to visualize what's going on and expedite my understanding
Im taking AP Calculus BC as a junior in high school and this helped me so much, ty 👍
You helped me past Calculus so far this year. Thank You.
Once again, Khan Academy saves my life
I actually literally screamed when I saw this THIS IS GOING TO SAVE MY LIFE
How are you now? Noticed this was 8 years ago
Man, I just passed Calc 1 this semester and I probably couldnt have done it without your help and some of your other videos. Thanx a ton bro!!
takin it way back with this one
Sheesh, this an OG khan vid
I have a calc final tomorrow and I'm p sure this video is the only reason I'll be able to graduate thanks for my life
this video is still useful to this day
thankyou
"I should be writing 'S(x)'--I shouldn't be lazy with my notation..."
Classic...
Thanks for the video!
I will pass my Calculus final thanks to your videos! Thank you! xD
like everyone else- you have helped me greatly and i expect a much higher grade on my test. Thankyou
Thank you. I just might make it through my calculus class :)
Thank you so much!! Helped me for my final!
Back when CZcams had a maximum time limit on problems involving minimums.
I swear my semester grade in calculus right now would be a -10% if it wasn't for these videos
Yeah even mine
Yeah even mine
i wish i saw this before my quiz last week. but, test is tomorrow and this was helpful!
wow, dude, you are so good I can learn more than in my class and english isn't even my native language.
Even though this is terrible to look at (lol) it's still the most helpful thing on CZcams
You have like the sexiest voice ever. And that voice saves millions of lives! Thank you!😍😍😍😍😍😆😆😆😆
I have to relearn this for a class after I already finished differential equations and thus give this video the 1000th like!
thanks so much this really helped!
Khan is my hero!
you never let me down ty
This is the most sass I have heard Sal have lmaooo that intro
While I love Khan the older videos really need a remake the 240p resolution is super hard to look at as well as read.
Thank you, good sir!
Doing gods work😭🤞🏽
Here is a quick note, there are actually 4 answers! Real:+4, -4 AND complex: 4i, -4i. (power 4 indicates there must be 4 solutions)
yes, to show if its a min or max
thank you so much this is my biggest problematic unit in calculus
YOURETHEBEST.
If you were my Calc Professor and my Chem Professor, NOBODY I REPEAT NOBODY WOULD FAIL NO MATTER HOW HARD THEY TRIED
i loved this ...thank you...
i subscribed because i found this extremely helpful.
Peace&Blessings.
my friend julss likes ur voice
AP CALC I AM COMING FOR UUUUUUUU
@username15219 you can... but it will probably take longer, i always use the 2nd derivative in case you are asked to find inflection points and so forth
it helps a little to decrease the screen size.
But I agree
Over a decade later and these videos are still being used
This helped me understand a basic idea of solving optimizations, so I thank you. Though would this same method be used when we take real world examples, such as finding the max volume of a box?
THANK YOU
THANK YOU
THANK YOU
lol i love this guys videos
You deserve a Nobel Prize.
THANK YOU MR. KHAN
out of his quick jokes - this has gotta take the cake 'save my electronic ink' - lmao!!!!!!! well apart from the infamous '(s)e^x, i sometimes think about this when i go to bed' - sal, keep up the good work, u share the unselfishness of the late nikola tesla and humorous side of einstein... thanks heaps... save my electronic ink, loool.....
Very helpful, thanks so much
YOUR MY HERO
MORE OPTIMIZATION PROBLEMS PLEASE!!!
nice. but when you did the second derivative test you couldve just used the first derivative and made and S prime number line
good one
Thank you alot, plz post more single variable calculus
OG
when you square root the 256 or any number that is positive you get a positive of negative number
thx gang
this looks really easy now
Sal, you are my best friend.
Thankyou!
No. Once you solve the derivative for x and get y, (at around 6:22) you are done with the problem. The rest is just checking to see you did-nt make a mistake.
thanks
Saving electronic ink. Ha ha
Omg this video is the best
Haven't started studying and I have a Calculus final tomorrow 9am.... CHALLENGE ACCEPTED
AWESOME!!!
This is the OG Kahn Academy... look at the quality lol
Thank you, now i won't fail my finals
Awesome
wouldn't it be easier to do it with the lagrange multiplier method ?
L ( x, y ) = x^2 + y^2 + lambda ( xy + 16 )
dL / dx = 2x + lambda ( y ) == > x = -(lambda )y / 2
dL / dy = 2y + lambda ( x ) == > y = - ( lambda )x / 2
dL / d(lambda ) = xy + 16 ==> = xy = - 16
( - lambda)^2 ( xy ) / 4 = - 16
lambda^2 = 4
lambda = 2 or - 2
x ( - x ) + 16 = 0
x^2 = 16
x = 4 or - 4
y = - 4 or 4
@leakedazaz I think he uses Paint and he puts a black background so it's easier to see
@leakedazaz i think he uses smoothdraw 3 actually
thank you very much!!!!
A company makes and sells X digital cameras/week. the weekly price-demand and cost equations are, P=400-.04X; C(x)=2000+160x.
(a) What price should a company charge for cameras, and how many cameras should be produced to maximize weekly income?
(b) what is the maximum revenue?
Can you please solve this word problem? One i see it solved i can figure out the pattern and apply it to the other similar ones i have :-)
Thanks
Could you use the first derivative test instead to determine extrema, to save the work of doing the second derivative?
Gonna fail but still gonna try for this test tomorrow.
Well Sal, i understand that you have a 10 minute capacity but that's actually the cap before you're allowed to enable advertisements on your videos. It would be good to profit yourself as well as others by teaching and making ad revenue.
Tip: Watch Sal Khan's videos in 1.5x speed always.
@LuisSlash Peru Corazon!
To Khan Academy: At the 5:00 min mark, isn't 2x^2 supposed to be 8x^4 rather than 2x^4 because you are also multiplying the coefficient?
He multiplies 2x by x^3. That's the same as multiplying 2*x*x*x*x which is just 2x^4
I just wish that the videos were in focus.
Why do I even bother going to college to study maths when I learn it here like in 10 minutes simple!
why is it that when my proff says this im very confused, but once I hear Sal explain it I feel stupid for not getting it the first time?