1. ## Calculus 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!

2. Hello, Sculthorp!

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 $x$ = the smaller number.
Then $x+100$ = the larger number.

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

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

And that is the function we must maximize.

Got it?

3. Thanks so much!!

OBAMA!!!!!