Optimization with Calculus 1

[username15219]

Could you use the first derivative test instead to determine extrema, to save the work of doing the second derivative?

[Haroids]

@username15219 Of course.

[Alive4Metal]

@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

[Exegete84]

I remember struggling with these.

[LoveThemMusic]

thank you!

[leakedazaz]

what software do u use to write that?

[hiddenice123]

@leakedazaz I think he uses Paint and he puts a black background so it's easier to see

[leakedazaz]

@hiddenice123 thanks

[maneprady21]

@leakedazaz i think he uses smoothdraw 3 actually

[retrorockie]

I actually literally screamed when I saw this THIS IS GOING TO SAVE MY LIFE

[spanishtrouble]

These and related rates are so annoying to wrap your head around for the first time

[luv4drums1]

damnnnn I was spazzing out saying "this makes no sense!"... but then i remembered the derivative of in my case (441/x) is -441/x^2, not 441/x^2.

[veeds74123]

thanks so much this really helped!

[farfigneutron]

Thank you. I just might make it through my calculus class :)

[asanchez1572]

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?

[ThePinkFlamingo305]

What if you want to maximize it?

[karkrashful]

@ThePinkFlamingo305 the same thing, once u get the critical values when u find the derivative, do the first derivative line test and find a maximum, thats when the sign of the derivative changes from + to - and thats your maximum value

[pratiksrc]

sal i think u should start using a mac :D

[Mrcyberboy18]

Is this the same thing as linearization?

[KenjiXD]

lol i love this guys videos

[Freakingeediot]

wow, dude, you are so good I can learn more than in my class and english isn't even my native language.

[hamman3509]

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!!

[Stanley81]

my friend julss likes ur voice

[ss340471]

awesome!!!!!!

[haseebahmed07518]

i shoudn't be lazy but anyway you get the point haha lmao

Anyway thanx

[greatdeath001]

Can you do an Optimization problem where you need to find the dimensions of a Rectangle inside a semicircle with a radius of 3?

[runback1983]

create philosophy vids please

[lolololort]

@runback1983

I'm not sure, but you might find some lectures on the MIT channel

[Killuminatismd]

Calc exam tommorow, chilling around watching ur vids

[ChristewieTV]

If you were my Calc Professor and my Chem Professor, NOBODY I REPEAT NOBODY WOULD FAIL NO MATTER HOW HARD THEY TRIED

[lukaboy2]

OMG thanks so much, your a savior!

[rayz3678]

Why do I even bother going to college to study maths when I learn it here like in 10 minutes simple!

[joemae1]

Thank you so much!! Helped me for my final!

[Metalmandy8]

YOUR MY HERO<3

[whydizz]

MORE OPTIMIZATION PROBLEMS PLEASE!!!

[LoVeLyLiNh529]

youre a dork dude,,

[princessdeander]

AWESOME!!!

[TheDennyvu]

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

[BlackieChan21]

@TheDennyvu lol exactly why im watching this

[HaloAsReligion]

@TheDennyvu Big woop.. my teacher gives easy examples, easy HW, but on the final she screws us over..

[vvbn7890]

@HaloAsReligion Story of my life bro.

KhanAcademy - You have contributed to my success so much over the past few months. Please dont ever retire.

[Sultanxxx123]

I LOVE YOU MY LAST NAME IS KHAN!

[ilordzammy]

@Sultanxxx123 MY DOGS NAME IS KUTHA!!!

[Sultanxxx123]

@ilordzammy OOLU KAY PUTAAY IS YOUR BROTHERS NAME LOL JK JK

[Jonnyistheman9000]

YOURETHEBEST.

[gigamuffin]

good video, but don't forget to test the critical numbers and restrictions on the variables in yor sum formula to determine which value will give you the minimum sum

[alaazahra]

love you

[XtagdaearthX]

nice. but when you did the second derivative test you couldve just used the first derivative and made and S prime number line

[bonitachica786]

THANK YOU

THANK YOU

THANK YOU

[murderXmeXsweetly]

You're wonderful. I can't even tell you how much these videos have helped out.

[YOitsNat]

Thank you so much. you are a great teacher, and you have great hand writting.

[LuisSlash]

ohh very good.....i practiced this problems in the UNI (UNIVERSIDAD NACIONAL DE INGENIERIA) LIMA PERU...GBY

[DkZeria]

@LuisSlash Peru Corazon!

[BrendaGoes123]

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?

[sublimefunk]

256 is not a function...its a constant.

you don't need to use the quotient rule

its just a constant times a variable

[deanaolles]

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!

[shadowflash9]

@BrendaGoes123

he rewrote the problem as a multiplication problem

(256)x(x^-2) and then he used the product rule which is just

the derivative of the first thing times the second thing

plus

the derivative of the second thing times the first thing

since in this case the derivative of the first thing (256) is zero,(thus rendering the entire first multiplication problem 'zero') we are left with the derivative of the second thing times the first thing.

[djenne08]

it is right, he made x sqaured into x to the -2 in order to get rid of the fraction...

[xyfaer]

that is when there is a variable on top and bottom of a quotient. in this case it is 256x^(-2)

[FreezingSun14]

@BrendaGoes123 instead of using that tedious formula, sal just brought down the 256 to be multiplied by x^-1 cuz 256/x=256x^-1. This way he could just use the power rule, not the quotient rule

[ZeroG004]

wow, calculus looks difficult. I understand some of the functions but I don't know where hes getting some of his numbers. I wish I was good with numbers =\

[msthickness2012]

You are seriously better than my Calc1 professor at FMU....Thanks for putting these videos up! You are my lifesaver!

[illmatic33]

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

[MacMacPherson1]

thank you so much

[speedracer300]

you are the man

[sasamuraki]

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.....

[Xlaxsauce]

thank you so much this is my biggest problematic unit in calculus

[KMedina619]

"I should be writing 'S(x)'--I shouldn't be lazy with my notation..."

Classic...

Thanks for the video!

[babyphat31]

OMG you definitely made everything much easier.

[19XmikeyX91]

thank you for the explanation i've missed a whole week of class but know i get this thanks

[sesshira25]

thank you. would you be able to do a volume one? i can do these but i have trouble with those... thank you

[gamblerkys]

save your electric ink haha!

[marcusjhung]

nice and clear.

[erika50]

Love the way u explain it..

one problem? it's too messy =/

[baylewis]

this looks really easy now

[linkbankai50]

thank you very much!!!!

[MrsSidneyCrosbyy87]

thank you so much from the bottom of my heart for doing this. i spend hours trying to figure out optimization and my exam is tomorow. i get it now. THANK YOU .

[Shapel]

i loved this ...thank you...

i subscribed because i found this extremely helpful.

Peace&Blessings.

[lindseykd91]

ummmm this WILL be the reason i don't fail my AP Calc exam. THANK YOU.

[crihans90]

what did you made on x2+256%x2

[thatguy4805]

like everyone else- you have helped me greatly and i expect a much higher grade on my test. Thankyou

[bubblegumrissa]

Oh my goodness, thank you so much! I thought I was going to fail my quiz tomorrow because I didn't get this stuff. Thanks!

[baphoring9999]

i really appreciated your hard work hope you make more of this things. watching your 10 min video is almost equal to 1hr lecture that i have with my teacher

[Gurupedia]

thanks...nice info...:)

[facedowninthedirt]

i wish i saw this before my quiz last week. but, test is tomorrow and this was helpful!

[JMAEspain]

what programme do you use to write on comp?

[natzo89]

He could just record himself writing on paint while using a drawing tablet.

[oaslam]

Thanks for doing all this.

[Waranle]

Thank you alot, plz post more single variable calculus

[AkashP4]

Thankx so much Sal!