calculus-applications-in-business3315.doc

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business world. The maximums and minimums of the curve of a

function have the slope of !, so the derivative of the e"uation is set

e"ual to ! to determine the input at the function#s optimal state. $or

example, in the case of an apartment complex company, a function

can be determined to %nd out the amount of money produced by the

number of apartment buildings sold, an e"uation of a simple

relationship. &eeping in mind the domain 'the number of apartments

actually available(, the function#s derivative reveals the critical points

that can be determined to be absolute maximums, absolute

minimums, or neither with the reinsertion of the values into the original

function. The use of derivatives and their role in optimization reveals

that the maximum pro%t does not necessarily come from renting out

allthe apartment buildings, as maintenance costs and other variables

need to be considered. )onse"uently, the analysis from the derivative

e"uations alerts the business owners to %nding a means of raising rent

costs or lowering maintenance costs to get maximum pro%t to full

resource capacity. The economic principle of marginal analysis is

bene%cial to brea-even analysis and pro%t maximization. The pro%t-

maximizing "uantity of output is achieved at the point where marginal

cost, the extra cost of production of a single unit of output, and

marginal revenue, the extra revenue generated by the sale of an

additional unit of product, are e"ual. The marginal revenue is formally

de%ned as the change in total revenue over the change in one unit of


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"uantity and can be represented as a derivative. The total revenue is

e"ual to the price demanded multiplied by the "uantity, so through the

product rule the marginal revenue is e"ual to the price demanded plus

the "uantity times the derivative of the price demanded. *ith this

information, the owners of a %rm can ascertain the pro%t-maximizing

"uantity based on its role as a monopoly or a competitive %rm and to

e+ciently organize its factors of production and exercise specialization.

Because the derivative gives the slope of a curve, it can be

applied to the curves commonly utilized in the business conference

room revenue and cost curves and stoc maret curves. graph of a

%rm#s total revenue for a period of time depicts changes in total

revenue while that of the cost depicts changes in costs with relation to

the level of output. The slope of the curve at a single value is

determined by the function#s derivative, and it can be used to

determine an increase or decrease in sales and proections for the

future. The attainment of slopes and instantaneous rates of change

can be used for stoc maret curves as well. The price history curve for

a %rm or corporation reveals the price of its shares at dierent points in

time, and the slope at a speci%c point indicates growth or decline,

further denoting the potential future success or failure of a business.

The same concept wors for other curves relevant in the business

arena, such asyield curves, which capture the overall movement of interest rates on


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bonds of different maturities. Curves can be evaluated by the important differential

calculus applications.

Business calculus can be applied to determine the e"uation and

graphical shape of a total cost curve, a function#s derivative, and other

aspects necessary or convenient for a business to now. /n addition to

measuring a function#s change with respect to that of its input, a

derivative is also a %nancial instrument that plays a role in the stoc

maret. /t is derived from an underlying asset, which is usually an

asset, event, index, or value. *ith the purchase of a stoc comes the

ownership of a small part of the company, an ownership that provides

an intrinsic value. 0erivatives traders over time exchange cash or

assets based upon the underlying asset, and they can in1ate stoc

values and increase their ostensible values.

2o matter which occupational %eld a student is interested in,

calculus and mathematics in general will play a role, apparent or

implicit, in its success. 3o instead of hoping to leave that calculus class

and dismissing its teachings, one must embrace calculus

wholeheartedly. To have a competency in mathematics is to be armed

with the proper tools to thrive in any %eld.


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B$B'$()*AP+

-Business Applications. /0 Sept 122.Pauls Online Math Notes. 14 (ct 1225

6http788tutorial.math.lamar.edu8Classes8Calc$8BusinessApps.asp#9.

Clayton, )ary :. :conomics principles ; practices. erivative. 122?. The Financial Dictionary. 14 (ct 1225 6http788financial=

dictionary.thefreedictionary.com8>erivative@calculus9.

'ane, Margaret. $nterview. 14 (ct 1225.

'au, effrey. -"otal *evenue and :lasticity. 32 un /55. University of Hawaii. 1? (ct

1225 6http788www1.hawaii.edu8rpeterso8demand.htm9.

"atum, Malcolm. -hat is a >erivatives Mar&etD // Sept 1225. Wise Geek. 13 (ct1225 6http788www.wisegee&.com8what=is=a=derivative=mar&et.htm9.

agner, +ans. -Bond ield Curve and the Stoc& Mar&et. 14 May 1225.Daily Markets.

13 (ct 1225 6http788www.dailymar&ets.com8stoc&s8122582481?8bond=yield=curve=and=the=stoc&=mar&et89.

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