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!
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 $\displaystyle x$ = 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?