How to Solve ANY Optimization Problem | Calculus 1

A step by step guide on solving optimization problems. We complete three examples of optimization problems, using calculus techniques to maximize volume given surface area, maximize area given perimeter, and to minimize distance on a curve from a given point. #calculus1 #apcalculus

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[WrathofMath]

CORRECTION: In problem 1, at 8:06, the written volume of 118 in^3 is incorrect. 6x6x3 = 108, and hence 108 in^3 is the correct volume.

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[samkim]

Hi, please add timestamps and video chapters into your videos. Thanks!

0:55 - Finding Dimensions of a box
8:33 - Guidelines for Maximum and Minimum Problems (Larson's Calculus)
9:44 - Finding Dimensions of a square fence
14:00 - Minimizing distance of a point from a parabola
19:47 - Summary

[punditgi]

We maximize our learning with Wrath of Math! 😊

[isobar]

This I can do...but when it comes to 'the calculus of variations' I'm lost! I have yet to see the original derivation of this concept by Leonard Euler explained in a way that is comprehensible to me. Math to me is just an enjoyable hobby...love your videos and thanks.

[rehor]

swear this dude doesn't blink the whole video it's throwing me off but its rly helpful thank u

[abdallahsaleh]

Hey! I do believe there was a miscalculation for the first question 6 x 6 x 3 is 108 in^3 not 118 in^3. Thanks for the video btw!

[thatoneuser]

11:50 shouldn't the interval be 0 < x < 1200 ?

[Ofek-sbot]

in the first question x can't be 0 because you divided by x, so the domain is 0<x<=sqrt108, also great video! you explained everything very well!

[tapstrafe]

Video was incredibly helpful and the steps were very well explained! Thank you so much!

[STEG_NO]

nice video helped me alot on my test hope i did good

[junchen]

Thank you so much for making this video. This video helped me a lot :)

[FacuFernandez]

"... but let's just use calculus" haha love it

[pipertripp]

Quick question... enjoyed working that last problem before watching. I used d as the primary function rather than the d^2 transformation. Got me thinking... in order to use a transformation to make the arithmetic easy, does the transformation need to be monotonic in nature so that we can say the the min/max of the transformation will occur at the same spot as for the original function? Does the original function also have to be monotonic?

[ibraxiv-_-]

For the last example why didn’t you use implicit differentiation for d^2 ?

[tibbar]

Screw these problems, finding the equations to these depends on the topic. Skipping this and related rates

[ikku]

I don't know mate, my local government thinks that the ceiling height of 2, 5 meters is optimal for a drywalled box, although people prefer much higher ceilings because they offer better living conditions mentally and physically. The real life height is even lower then 2, 5 because most of the communications are built into the ceilings these days, so 2, 5 isn't actually even 2, 5.
My bet would be, that optimal is a sum of educated choices that defines and eliminates the widest rage of problems, that may not be limited to a waste of material.

[dasnerth]

How does the x equal the 1/2 y^2. Thats so confusing to me 15:51

[resvolver]

I'm confused, shouldn't the surface area formula be 2x^2 + 4xh = 108 in^2?

[Francis-xqnw]

and i wanna maximize the math for my class schedule