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Question
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
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Solution
f(x) = 2x3 – 6x2 + 6x + 24
∴ f′(x) = 6x2 – 12x + 6
= 6(x2 – 2x + 1)
= 6(x – 1)2
f(x) is strictly increasing, if f′(x) > 0
∴ 6(x – 1)2 > 0
∴ (x – 1)2 > 0 for all x ∈ R, x ≠ 1
Thus, f(x) is strictly increasing for x ∈ R – {1}.
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