Snell's Law : A Calculus Based Proof

[ravipratapmatli]

Dear patrick
ur xplanation is u very much.
u r my

[jirobow]

my man patrick quenching my curiosity from 8 years in the past.

[patrickjmt]

correct, i do not control the ads at all.

[tgdhsuk]

what do you mean about something to do with the minimum at 1:38

[patrickjmt]

i agree, i do not think this problem would be unreasonable

[patrickjmt]

it represents the minimum time to get along the path APB

[LudwigSpiegel]

I wish I had a teacher like you back in the days....

[sjsawyer]

When you use the chain rule on a function you leave the argument of the function alone and then differentiate it. For example the derivative of sin(3x) is cos(3x) * 3. Likewise the derivative of exp(x+4) is exp(x+4)*(1+0) = exp(x+4). That probably didn't help. And x isn't a constant, which is why he differentiated with respect to x.

[patrickjmt]

you are finding critical numbers which helps find maximums / minimums

[patrickjmt]

sometimes i buy paper and just throw it away in the garbage. or i litter with it and just throw it out the window as i drive my gas guzzling hummer down the road.

[rctwik]

did he take the turning point (minimum) because light takes the fastest root possible or something?

[rickshawty]

Thanks a lot that was extremely helpful

[patrickjmt]

i can hear them with no problem, but i will look into it.

[daraudobong]

This really helped me out, thank you and God bless you!

[bin]

This proof is incomplete: after finding the critical point you need to prove that the second derivative is necessary positive in order for this to be an absolute minimum on an infinite interval

[alexleviyev]

why do you keep all the constants when you take the derivative? dont they cancel out? and why is x a constant i dont understand D:

[schumerthd]

Once you started to show the proff I remember I had to write a program that involved snail law.

[macaron]

thanks for this. I can use it in my math project

[jchrdan]

nice proof but why did we take the derivative and write =0?

[aednil]

i don't think the uploader of a video has any influence on what advertise exactly is going to be on his video. you'd have to ask you tube what is up with mormon ads.