The most appropriate choice for maxima or minima will be given by-
Length of field of largest dimension = 1200 ft
Width of field of largest dimension = 600 ft
What is maxima or minima?
Suppose a function is increasing for some values of the domain, changes its slope and then decreases. The point where the function changes slope is the point of maxima of the function.
Suppose a function is decreasing for some values of the domain, changes its slope and then increases. The point where the function changes slope is the point of minima of the function.
Here,
Let the length of the rectangle be l ft. and width of the rectangle be x ft.
Length of fencing = [tex](x + l + x)[/tex] ft
= [tex](2x + l)[/tex] ft
By the problem,
[tex]2x + l = 2400\\l = 2400 - 2x[/tex]
Area of the field (A) = [tex]lx[/tex] sq. ft
=[tex](2400 - 2x)x[/tex]
= [tex]2400x - 2x^2[/tex] sq.ft
[tex]\frac{dA}{dx} = \frac{d}{dx}(2400x - 2x^2)\\2400 - 4x[/tex]
[tex]\frac{dA}{dx} = 0[/tex]
[tex]2400 - 4x = 0 \\4x = 2400\\x = \frac{2400}{4}\\[/tex]
[tex]x = 600[/tex] ft.
For checking maxima or minima double derivative has to be calculated[tex]\frac{d^2A}{dx^2} = \frac{d}{dx}(2400 - 4x)\\= -4 < 0[/tex]
Hence the area is maximum at x = 600 ft
[tex]l = 2400 - 2\times 600\\l = 2400 - 1200\\[/tex]
[tex]l = 1200[/tex] ft.
Length of field of largest dimension = 1200 ft
Width of field of largest dimension = 600 ft
To learn more about maxima and minima of a function, refer to the link-
https://brainly.com/question/28859877
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Complete Question
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