SOLUTION: Bob has 3000 feet of fencing available to enclose a rectangular field. A. express the area A of rectangle as a function of x where x is the length of rectangle. B. for what valu

Question 40032: Bob has 3000 feet of fencing available to enclose a rectangular field.
A. express the area A of rectangle as a function of x where x is the length of rectangle.
B. for what value of x is the area largest?
C. what is the maximum area?
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
> 2. Bob has 3000 feet of fencing available to enclose a rectangular field.
>
> a. express the area A of rectangle as a function of x where x is the length
> of rectangle.
L=X...PERIMETER=L+B+L+B=2(L+B)=2(X+B)=3000
X+B=1500
B=1500-X
AREA =A= L*B=X(1500-X)
> b. for what value of x is the area largest?
A=X(1500-X)=-(X^2-1500X)=-(X^2-2*X*750+750^2)+750^2
A=750^2-(X-750)^2
HENCE THIS WILL BE MAXIMUM WHEN X=750
> c. what is the maximum area.
> MAXIMUM AREA =750^2-0=750^2=562500
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