A farmer has an 80m length of fencing. He wants to use it to form
three sides of a rectangular enclosure against an existing wall which
will be the fourth side.

a) Denote the length of one of the sides by x, what is the area of
the enclosure?
b) By use of differentiation or otherwise and the maximum area of
the enclosure.

I do not know how I can get the answer by using differentiation .. Help me please !

Originally Posted by yanirose
A farmer has an 80m length of fencing. He wants to use it to form
three sides of a rectangular enclosure against an existing wall which
will be the fourth side.

a) Denote the length of one of the sides by x, what is the area of
the enclosure?
b) By use of differentiation or otherwise and the maximum area of
the enclosure.

I do not know how I can get the answer by using differentiation .. Help me please !
.
Hint: The maximum of the area is going to be where the derivative is 0. (Technically you should check that this is actually a maximum.)

-Dan

Hint: If you decide to forego the calculus in lieu of "otherwise," then find the axis of symmetry of the resulting parabolic area function.

Have you made a sketch? Have you determined the area as a function of one variable?