The function $f(x)=x^3-3x$ is :

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Relations and Functions

Question:

The function $f(x)=x^3-3x$ is :

Options:

Increasing in (0, ∞) and decreasing in (-∞, 0)

Decreasing in (0, ∞) and increasing in (-∞, 0)

Decreasing in (-∞,-1] ∪ [1, ∞) and increasing in (-1, 1)

Increasing in (-∞, -1] ∪ [1,∞) and decreasing in (-1, 1)

Correct Answer:

Increasing in (-∞, -1] ∪ [1,∞) and decreasing in (-1, 1)

Explanation:

The correct answer is Option (4) → Increasing in $(-∞, -1] ∪ [1,∞)$ and decreasing in $(-1, 1)$

$f(x)=x^3-3x$

$f'(x)=3x^2-3=0⇒x=1,-1$

using wavy curve method

f(x) is increasing in $(-∞,-1]∪[1,∞)$

decreasing in $(-1, 1)$