Maharashtra State BoardHSC Arts 12th Board Exam
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Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing - Mathematics and Statistics

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Sum

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}.

Concept: Increasing and Decreasing Functions
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