If $f\left( x \right) = 3{x^4} + 4{x^3} - 12{x^2} + 12$, then $f\left( x \right)$ is

Increasing in $\left( { - 2,{\rm{ }}0} \right)$ and in $\left( {1,\;\infty } \right)$

Increasing in $\left( { - \infty ,\; - 2} \right)$ and in (0, 1)

Decreasing in $\left( { - 2,{\rm{ }}0} \right)$ and in (0, 1)

Decreasing in $\left( { - \infty ,\; - 2} \right)$ and in $\left( {1,\;\infty } \right)$

JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

f\left( x \right) = 3{x^4} + 4{x^3} - 12{x^2} + 12

, then

f\left( x \right)

View answer and explanation

Correct option: B

Increasing in

\left( { - 2,\mathrm{ }0} \right)

and in

\left( {1,\;\infty } \right)

Option B is correct because the function is increasing where its derivative is positive, which occurs in the intervals (-2, 0) and (1, ∞).