If $f(x)=-3x^2,$ then $f(x)$ is :

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

If $f(x)=-3x^2,$ then $f(x)$ is :

Options:

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

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

Increasing in $\left[-\frac{1}{3}, ∞\right),$ decreasing in $\left(-∞,\frac{-1}{3}\right]$

Decreasing for all real values of x

Correct Answer:

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

Explanation:

$f(x)=-3x^2$

differentiating wrt (x)

$f'(x)=-6x=0$ (at x = 0)

Using wavy curve method

so increasing in (-∞, 0), decreasing in (0, ∞)