# Math Help - Maxima And minima

1. ## Maxima And minima

A farmer has 40 m of fencing with which to enclose a rectangle pen.
Given the pen is x cm wide,

a). show that the area is (20x -x^2)m^2
b) Deduce the maximum area that he can enclose.

2. Originally Posted by mazy22a

A farmer has 40 m of fencing with which to enclose a rectangle pen.
Given the pen is x cm wide,

a). show that the area is (20x -x^2)m^2
b) Deduce the maximum area that he can enclose.
perimeter, $P = 2(L+W)$

$40 = 2(L + x)$

$20 = L + x$

$L = 20 - x$

$A = LW$

$A = (20 - x)x = 20x - x^2$

if you graph the area function, it will look like an inverted parabola. the maximum will be located at the parabola's vertex.

Do you know how to find the x-value for the vertex of a parabola?

3. ## thanks

yeh maximum is 100 m^2

worked it out by completing the square on

- X^2 - 20x

cheers mate