NTA Abhyas JEE Main2020MathematicsApplication of DerivativesPractice

If f x = 3 x 4 + 4 x 3 - 12 x 2 + 12 , then f ( x ) is

Options

Aincreasing in − ∞ , − 2 ∪ 0 , 1
Bincreasing in − 2 , 0 ∪ 1 , ∞
Cdecreasing in − 2 , 0 ∪ 0 , 1
Ddecreasing in - ∞ , - 2 ∪ 1 , ∞

Correct answer

B. increasing in − 2 , 0 ∪ 1 , ∞

Step-by-step solution

Since, f ( x ) = 3 x 4 + 4 x 3 - 12 x 2 + 12 f ′ x = 12 x 3 + 12 x 2 - 24 x = 12 x x - 1 ( x + 2 ) The above expression it is clear that f x is increasing in − 2 , 0 ∪ 1 , ∞ and decreasing in - ∞ , - 2 ∪ 0 , 1

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