The interval in which the function $f(x) = 2x^3 + 3x^2 − 12x + 1$ is strictly increasing, is

$(-∞,-2) ∪ (1,∞)$

The correct answer is Option (1) → $(-∞,-2) ∪ (1,∞)$

$f(x)=2x^{3}+3x^{2}-12x+1$

$f'(x)=6x^{2}+6x-12=6(x^{2}+x-2)=6(x+2)(x-1)$

Critical points: $x=-2,\;x=1$. Sign analysis of $f'(x)$ gives $f'(x)>0$ for $x\in(-\infty,-2)\cup(1,\infty)$.

The function is strictly increasing on $(-\infty,-2)\cup(1,\infty)\,$.