Zombie CancerA cozy riverside village, Psychotropic Town, is about to be quarantined because of a

deadly outbreak of an unnamed virus. The virus is Angry Duck Eating Soap (ADES). In order to protect the neighboring village,

you will need to construct a fence around this town. Of course, because the mayor

of Psychotropic Town is a money grubbing cretin, he wants you to construct it with

1000 feet of fence and create the largest area possible. Since a river borders one

side of the town, you won't need to fence that side off. People with ADES can't

swim... duh...

Variable & Equation Declaration

x = lengthy = width

A = x*y (Primary)2x + y = 1000 (Secondary)

Solving for width(y)

2x + y = 1000y = -2x+1000

Creating a New Area Equation

A = (x)(1000-2x)A = 1000x – 2x22

Differentiating the Area Equation

A = 1000x – 2x22

A' = 1000 – 4x

0 = 1000 – 4x-1000 = -4x

X = 250

0Length is 250 feet.

Solving for width

1000 = 2x + y1000 = 2(250) + y

1000 = 500 + y500 = y

Width is 500 feet.

Proving ourselves

Second Derivative TestA'' = -4

(it is concave down, meaning it's a relative maximum)

Happy F-Bomb Factory

Happy F-Bomb factory is making a new product, the H-Bomb. In order for the shipping to

commence, an appropriate and environment-friendly cost plan has to be mapped out. Determine the production level that will

maximize the profit for the company with cost and demand functions: C(x)=84+1.26x-

0.01x2+0.00007x3 and p(x)=3.5-0.01x and What is the maximum profit?

Variable and Equation Declaration

x = units P = profit (R – C)p(x) = 3.5 - .01x

C = C(x) = 84+1.26x-.01x2-.00007x3

R = p(x)[x] = 3.5x-.01x2

Solving for Profit

P = R – CP = 3.5x – 0.01x2 – 84 – 1.26x + 0.01x2 – 0.00007x3

= -0.00007x3 + 2.24x - 84

Solve for x!

P' = -0.00021x2 + 2.24x2 = 10666.666

x = 103.28

Insert x into equation

P(x) = -0.00007x3 + 2.24x -84P(103.28) = 70.23

Proof of PURCHASE !$#@

P''(x) = -.00042xP''(103.28) = -0.0433776

Negative = Maximum = Concave Up = Yeah

Conclusion

Using derivatives allow you to find great deals on products, and how much (or little) of stuff you have to do for the most (or little) of something

else!

It also allows Mrs. Lustgraaf to derive the maximum possible grade for this presentation!!