Hey!

The difference between two numbers in 100. Find the numbers given that the square of the larger exceeds 5 times the square of the smaller by a maximum amount.

Any help is greatly appreciated!

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- Jan 21st 2009, 07:41 AMSculthorpCalculus Q
Hey!

The difference between two numbers in 100. Find the numbers given that the square of the larger exceeds 5 times the square of the smaller by a maximum amount.

Any help is greatly appreciated! - Jan 21st 2009, 08:38 AMSoroban
Hello, Sculthorp!

Quote:

The difference between two numbers is 100.

Find the numbers given that the square of the larger exceeds

5 times the square of the smaller by a maximum amount.

Let $\displaystyle x$ = the smaller number.

Then $\displaystyle x+100$ = the larger number.

The required difference is: .$\displaystyle A \:=\:(x+100)^2 - 5x^2$

. . So we have: .$\displaystyle A \:=\:-4x^2 + 200x + 10,\!000$

And*that*is the function we must maximize.

Got it?

- Jan 21st 2009, 02:09 PMSculthorp
Thanks so much!!

OBAMA!!!!!