If 2x+y=10 and A=xy, find the maximum value of A.

Question

blockcolder · Answer

From the first equation, we have $y=10-2x$.
Then, $A(x)=x(10-2x)=10x-2x^2$.
Now, I assume you know how to find the maximum of this quadratic. :)

anonymous · Answer

I did it this way but the answer isn't correct! :(

blockcolder · Answer

The maximum value of A is attained when x=5/2. There, A=25-(25/2)=25/2.
You mean to say this isn't correct?

anonymous · Answer

Your answer is correct. How did you do it? I didnt get it. I did it this way:
dA/dx= 10 - 4x
Then a second derivative for the the max value :
dA ^2/ dx^2 =-4

anonymous · Answer

And i got a wrong answer.

blockcolder · Answer

$\Large \frac{d^2A}{dx^2}=-4$ just implies that whatever critical point you get will yield a maximum. (Second Derivative Test)
Now, for said critical point, you need to set $\Large \frac{dA}{dx}=0$, then chug whatever x you get here into A(x).

anonymous · Answer

Oook !! I got it! Thanks alot and sorry for asking again and again! :)

blockcolder · Answer

It's okay. :)

anonymous · Answer

:)