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Ganezh [65]
3 years ago
15

A piece of wire 27 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral tria

ngle.
(a) How much wire should be used for the square in order to maximize the total area?
(b) How much wire should be used for the square in order to minimize the total area?
Mathematics
1 answer:
Anna71 [15]3 years ago
6 0

Answer:

a

Step-by-step explanation:

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Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,

f\left(f^{-1}(x)\right) = x

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So, we have three subsets over which f(x) can be considered invertible.

• (-∞, -1/√3)

• (-1/√3, 1/√3)

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\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}

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x³ - x = 0

x (x² - 1) = 0

x (x - 1) (x + 1) = 0

x = 0   or   x = 1   or   x = -1

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• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or

• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)

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