Question 4 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at August 14, 2026 by

The interval on which the function f (x) =Ā  2x 3 Ā  + 9x 2 Ā  + 12x - 1Ā is decreasing is:

(A) [-1,āˆž) Ā 

(B) [ā€“2, ā€“1]

(C) (-āˆž,-2] Ā 

(D) [ā€“1, 1]

Ā 

This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives

The interval on which function f(x) =Ā  2x3Ā + 9x2 + 12xĀ  - MCQ Class 12 - NCERT Exemplar - MCQs
part 2 - Question 4 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives
part 3 - Question 4 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives

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Transcript

Question 4 The interval on which the function f(š‘„) = 2š‘„3 + 9š‘„2 + 12š‘„ - 1 is decreasing is: (A) [āˆ’1,āˆž) (B) [ā€“2, ā€“1] (C) (āˆ’āˆž,āˆ’2] (D) [ā€“1, 1] f(š‘„) = 2š‘„3 + 9š‘„2 + 12š‘„ - 1 Calculating fā€™(š’™) fā€™(š‘„) = 6š‘„2 +18š‘„ + 12 - 0 fā€™(š‘„) = 6(š‘„2+3š‘„+2) fā€™(š‘„) = 6(š‘„2+2š‘„+š‘„+2) fā€™(š‘„) = 6(š‘„(š‘„+2)+1(š‘„+2)) fā€™(š’™) = 6(š’™+šŸ) (š’™+šŸ) Putting fā€™(š’™) = 0 6(š‘„+1) (š‘„+2) = 0 (š‘„+1) (š‘„+2) = 0 So, š’™ = ā€“1 , ā€“2 Plotting points on number line Hence, f is decreasing for the interval (āˆ’2, āˆ’1). So, the correct answer is (B)

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