Area a(w)= [tex] -w^2+100w [/tex] where w is the width
Area is in quadratic form.
To find maximum are we need to find the vertex.
a(w)= [tex] -w^2+100w [/tex]
To find vertex we use formula w= [tex] \frac{-b}{2a} [/tex]
a= -1 and b = 100
So w = [tex] \frac{-100}{2(-1)} [/tex] = 50
We will get maximum area when width w= 50m
To find maximum are we plug in 50 for w and find a(50)
a(w)= [tex] -w^2+100w [/tex]
a(50)= [tex] -50^2+100(50) [/tex]
a(50)= -2500 + 5000
= 2500
So maximum area is 2500 square meter and the dimensions are length = 50m , width = 50m
