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Question
Test whether the following functions are increasing or decreasing : f(x) = 2 – 3x + 3x2 – x3, x ∈ R.
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Solution
f(x) = 2 – 3x + 3x2 – x3
∴ f'(x) = `d/dx(2 - 3x + 3x^2 - x^3)`
= 0 – 3 x 1 + 3 x 2x – 3x2
= – 3 + 6x – 3x2
= –3(x2 – 2x + 1)
= – 3(x – 1)2 ≤ 0 for all x ∈ R
∴ f'(x) ≤ 0 for all x ∈ R
∴ f is decreasing for all x ∈ R.
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