A farmer has 1,200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence a
long the river. Write the function that will produce the largest area if x is the short side of the rectangle. f(x) = 1200x − x2
My answer choice. Is this correct? ->f(x) = −2x2 + 1200x
f(x) = x2 − 1200
f(x) = 2x2 − 1200
Yay, derivitives I'mma ignore that x is the shorter side because I don't know which one has to be shorter yet
we need to find the max area but with 3 sides
area=LW let's say the sides are z and y zy=area
and the relatiionship between them is hmm, z+2y=1200 because one side has no fencing so z+2y=1200 solve for z z=1200-2y sub for z in other
(1200-2y)(y)=area expand 1200y-2y²=area take derivitive 1200-4y=dy/dx area max is where dy/dx goes from positive to negative solve for where dy/dx=0 1200-4y=0 1200=4y 300=y
at y<300, dy/dx<0 at y>300, dy/dx>0 so at y=300, that is the max
then z=1200-2y z=1200-2(300) z=1200-600 z=600
so then z=600 y=300 300<600
so the shorter side would be y
so then we see our choices and noticed that erm I think it is f(x)=1200x-2x² takind the derivitive yeilds none of the others
