Jason plans to fence a rectangular area with 180 meters of fencing. He has written the formula A = w(90 - w) to express the area in terms of the width w. What is the maximum possible area enclosed with his fencing?How do you work this out?
A = w(90 - w)
maximum area, take the derivative and solve for w.
A = w(90 - w)
A = 90 w - w^2
(0 = 90 - 2w )%26lt;-derivative
-90 = -2w
w = 45 meters
plug in 45 to calculate the area
A = w(90 - w)
A = 2025 m^2How do you work this out?
Differentiate the function given to get:
dA/dw = 90 - 2w
At max area, dA/dw = 0.
Hence, let 90 - 2w = 0
w = 45
Max A = 45(90 - 45) = 2025 m^2
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