Question

Find the values of x for which the function f(x) = 2x³ – 6x² + 6x + 24 is strictly increasing

Answer 1

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}.