Calculus: Applied Problems in Business with Differentiation

[@Discovery_and_Change]

Problem 1: 0:18 Demand function 0:54 Maximize a profit function 0:57 Maximizing a function is not too hard, we take the derivative 1:06 What's the profit function? 2:05 Let's set up the profit function 2:37 Take the derivative 3:08 To solve derivative, set to 0 and solve for X 3:58 We need to find the price per unit, not just the number of units 4:12 Plug in to demand function Problem 2: 4:47 (begins)

[@1NinjaSamurai]

Not taking this class, but it was a pleasure to watch.

[@Fiandrea9]

I was gonna take but after watching this video I`m like nahhh

[@JasonLayton]

I don’t understand how a business could ever know the demand function in the first place.

[@chuka331]

market research

[@JasonLayton]

chuka centa can you provide a real world example of the deriving of a demand function?

[@driedmango1914]

Super simple answer: Experimenting with different price points.

[@trevor4995]

@@JasonLayton Gonna answer this because I was interested in your question. An example of finding the demand function would be (and this is a very very simple example) a company making a new game and trying to find how many people will buy it in the first month. So the company would gather sales data of other games in the same genre/graphics style/target market and use that data to predict a general number of potential sales and a price at which it should sell the game. Then, through a marketing campaign, the company would generate demand and exposure for the game to hopefully make people want to buy it. Then, through surveying, the company would be able to estimate how many people are interested in buying the game at launch, a month after, after an update, etc. and use that data in combination with the rest to predict sales. It is a very complex process which is much more in-depth than I've described, but I hope it gives you a general idea.

[@driedmango1914]

Trevor that’s a good example for estimating demand of a new product. However consider the example of a grocery store obtaining the demand function for apples: you could do so by simply experimenting with different price points and measuring the units sold at various prices. You would of course have to hold other factors constant, and it gets more complicated I’m sure.

[@mostafauwk7896]

thank my prof I follow you from Egypt 💜💜💪

[@gnimnuh6570]

Very good! Clear and nice handwriting

[@dopilus]

*_Excellent_* refresher man. So thankful for this upload: much* appreciated! You've got yourself Subscriber Mr. Schmidt. CHEERS

[@osamadupe1018]

How did you change 55 over root X times X😩

[@Alma_in_Florida]

I was scared to take this class but after this I’m not as intimated…whewww

[@nirvanichand9352]

Sir, how do we calculate for how long should a company operate?

[@lostintheclouds8719]

You explain this better than my teacher lol

[@akirashepherd9714]

What does the 55 represent? I was wondering if I could use this problem for my own business. Considering that 55 pre-determines the number of units you're making (and I personally want to sell 1,000 units of what I've made) how do I apply this? What should I replace 55 with in my case? Is it perhaps how many people are interested in buying from me?

[@KingDuken]

Akira Shepherd Late response but maybe helpful for future watchers. 55 is just a constant of a function that represents some type of demand. It’s not clear how or why the demand trend is what we saw but for example sake, that’s what the curve for demand turns out to be. It’s just a characterization for an arbitrary demand.

[@merc2413]

Im majoring in accounting, and my counselor put this course as one of the classes to take in upcoming semesters, but after watching this i wont take it, i dont see what accounting has to do with this, accounting just involves basic math, adding, subtracting, dividing in a fraction

[@alexmoretti8178]

Don’t you need the course to major in accounting tho? Or will you change your major

[@josephorossi]

accounting gives you the things hes solving for. they correlate a lot actually. this involves finding the numbers. in accounting, mostly managerial, the numbers are already given to you, you just have to put them in the right place in the data table, label them correctly, and do your arithmetic properly. with business calc, you find those numbers THEN account for it. this is why we need to take this course.

[@J10-f4s]

@@josephorossi hi’ don’t know if you’ll see my message but would appreciate your input. In order for me to get a degree in business administration and economics I need to take calculus for managerial life etc etc or I can take finite math and just get my business administration degree. Do you believe this calculus class is worth it?

[@BC-2]

I will so take your word for it

[@TheHermitHH]

What would 55 represent in a business stance?

[@iyeanna]

Hi Larry, What if you will determine the price and quantity in terms of €t(tax) and also determine the maximised profit in terms of €t.. We dont know the tax.. and then how would i solve for t? Thanks

[@additios125]

Please help me, this is driving me crazy. How did you simplify R(x) = (55/√ x) * x into R(x) = 55√ x (1:56) I am eager to learn mathematics, but I don't get those rules. Am I supposed to just remember that (J/√ H) * H = J√ H Can someone explain me this 'simplification' coz it's making things only more complicated for me.

[@gatt6597]

just multiply both sides ( up and down ) by root(x) you'll get 55*root(x)*x / root(x)*root(x) which means 55*root(x)*x / x then remove both x and you'll get 55*root(x) :D

[@additios125]

Info 4 evah omg, see, that's how bad I am xD Thank you so much for clearing tnat up!

[@SaltineChips]

How About Vector Fields? Just Kidding

[@urvifood6105]

Wait wouldn’t it be 55-sqrt (x)

[@thebaconguy5746]

No because 55x/sqrt(x) is basically 55x/x^1/2 which would leave you with 55 x^1/2 when you subtract exponents or 55sqrt(x)

[@Flaystray]

Why would it ever be useful to find the marginal profit when you can just use the original function

[@shaun_b]

I came to learn, and i receive headache