Please help me solve the following
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, $\displaystyle P = 2(L+W)$
$\displaystyle 40 = 2(L + x)$
$\displaystyle 20 = L + x$
$\displaystyle L = 20 - x$
$\displaystyle A = LW$
$\displaystyle A = (20 - x)x = 20x - x^2$
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?