Need work check

A farmer has 400 feet of fencing and wants to enclose a rectangular pasture. One side of the pasture is along a river and does not need fencing. What should the deminsions of the rectangular pasture be, so as to maximize the enclosed area?if on

I have it as x+2L=400
Solve for L= -.5x+200
A= x*L
A=-.5X^2+200X
dA=-x+200 x=200

thus the maximum area is 200*100

Did I do this properly?

Question

Need work check

A farmer has 400 feet of fencing and wants to enclose a rectangular pasture. One side of the pasture is along a river and does not need fencing. What should the deminsions of the rectangular pasture be, so as to maximize the enclosed area?if on

I have it as x+2L=400
Solve for L= -.5x+200
A= x*L
A=-.5X^2+200X
dA=-x+200 x=200

thus the maximum area is 200*100

Did I do this properly?

anonymous · Answer

yes.. but how do you know it's a max and not a min?  (this is something my teacher always asked because I always assumed it is...)

anonymous · Answer

because if I plug it back into A it gives me a positive number?

anonymous · Answer

good. you do the first deriv test.

anonymous · Answer

lol plus I could check increasing decreasing but thats just annoying lol

anonymous · Answer

yep...

anonymous · Answer

thats for helping me understand that concept a little more i never even thought about it that way!

anonymous · Answer

yw.:)