Find two numbers whose products is -16 and the sum of whose squares is a minimum. Practice this yourself on Khan Academy right now: www.khanacademy.org/e/optimiz...
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.
***** 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?
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!!
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?
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!
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.
@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
Around 4 min how or why did you get x-³ from? I get the 2x+(256) (-2) but the x-³ negative 3 thing is confusing me.. thanks ahead of time for the response.
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.....
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
also instead of doing the second derivative (concavity) test, can you just use the first derivative for the first derivative test and test for local minimum? also when you're doing 1st derivative do you also have to check for absolute max/min?
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.
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.
“Save my electronic ink” 😂
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?
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.
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!!
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!!
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?
You're wonderful. I can't even tell you how much these videos have helped out.
You helped me past Calculus so far this year. Thank You.
I swear.. Khan Academy has saved my life. x.x
I was sick during the optimization unit, my test is in two days, and my final is in a week. Bless you.
I always graph these once I find the equation, it helps me to visualize what's going on and expedite my understanding
Khan is my hero!
like everyone else- you have helped me greatly and i expect a much higher grade on my test. Thankyou
Thank you so much!! Helped me for my final!
I would just like to take a moment recognize the amazing "y^2" at 1:30
i loved this ...thank you...
i subscribed because i found this extremely helpful.
Peace&Blessings.
Once again, Khan Academy saves my life
takin it way back with this one
thanks so much this really helped!
Thank you. I just might make it through my calculus class :)
Calc exam tommorow, chilling around watching ur vids
you never let me down ty
THANK YOU MR. KHAN
Thank you, good sir!
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
I will pass my Calculus final thanks to your videos! Thank you! xD
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?
wow, dude, you are so good I can learn more than in my class and english isn't even my native language.
Very helpful stuff for the machine learning students
i wish i saw this before my quiz last week. but, test is tomorrow and this was helpful!
Even though this is terrible to look at (lol) it's still the most helpful thing on TH-cam
Doing gods work😭🤞🏽
this video is still useful to this day
thankyou
YOUR MY HERO
You have like the sexiest voice ever. And that voice saves millions of lives! Thank you!😍😍😍😍😍😆😆😆😆
Very helpful, thanks so much
Sheesh, this an OG khan vid
Back when TH-cam had a maximum time limit on problems involving minimums.
THANK YOU
THANK YOU
THANK YOU
I have to relearn this for a class after I already finished differential equations and thus give this video the 1000th like!
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
Thankyou!
YOURETHEBEST.
Omg this video is the best
AWESOME!!!
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!
Im taking AP Calculus BC as a junior in high school and this helped me so much, ty 👍
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
good one
thank you so much this is my biggest problematic unit in calculus
lol i love this guys videos
thanks
You deserve a Nobel Prize.
MORE OPTIMIZATION PROBLEMS PLEASE!!!
This is the most sass I have heard Sal have lmaooo that intro
it helps a little to decrease the screen size.
But I agree
While I love Khan the older videos really need a remake the 240p resolution is super hard to look at as well as read.
Awesome
Sal, you are my best friend.
@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
thx gang
yes, to show if its a min or max
my friend julss likes ur voice
Could you use the first derivative test instead to determine extrema, to save the work of doing the second derivative?
Thank you alot, plz post more single variable calculus
OG
How can I save Math videos to an external hard drive instead of them defaulting to my download folder on my C drive?
Around 4 min how or why did you get x-³ from? I get the 2x+(256) (-2) but the x-³ negative 3 thing is confusing me.. thanks ahead of time for the response.
"I should be writing 'S(x)'--I shouldn't be lazy with my notation..."
Classic...
Thanks for the video!
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
U also have to find the domain?
what software do u use to write that?
this looks really easy now
AP CALC I AM COMING FOR UUUUUUUU
Over a decade later and these videos are still being used
nice. but when you did the second derivative test you couldve just used the first derivative and made and S prime number line
why is ^ -3 a positive ^4 when brought to the other side? would it not be ^-4
This is the OG Kahn Academy... look at the quality lol
Isnt x and y always equal to sqroot of the product?
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)
@leakedazaz I think he uses Paint and he puts a black background so it's easier to see
mine is tomorrow :O
what did you made on x2+256%x2
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.....
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
Wait, if -4 for x is also a solution, then the second derivative is a complex number? Or am I just confused?
Isn't there another minimum in x = -4? The result in the 2nd derivative is the same than for x = 4.
@leakedazaz i think he uses smoothdraw 3 actually
are you sure you took the derivative right for 256 divided by x squared. isn't the formula f prime of g minus g prime of f over g squared?
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
also instead of doing the second derivative (concavity) test, can you just use the first derivative for the first derivative test and test for local minimum? also when you're doing 1st derivative do you also have to check for absolute max/min?
Yep, absolutely!
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.
when you square root the 256 or any number that is positive you get a positive of negative number