The function $f(x)=2x^3+3x^2-12x+1$ is s

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Relations and Functions

Question:

The function $f(x)=2x^3+3x^2-12x+1$ is strictly increasing in :

Options:

[-2, 1]

(-∞, -2) ∪ (1, ∞)

(-∞, 1]

(-∞, -1] ∪ [2, ∞]

Correct Answer:

(-∞, -2) ∪ (1, ∞)

Explanation:

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

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

$f'(x)=6x^2+6x-12=0$

$6(x+2)(x-1)=0$, $x=1,-2$

Using wavy curve

f(x) strictly increasing in $(-∞, -2)∪(1, ∞)$