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Question 17 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at March 22, 2023 by

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

(A) [-1,∞)  

(B) [–2, –1]

(C) (-∞,-2]  

(D) [–1, 1]

Β 

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

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Transcript

Question 17 The interval on which the function f(π‘₯) = 2π‘₯3 + 9π‘₯2 + 12π‘₯ - 1 is decreasing is: (A) [βˆ’1,∞) (B) [–2, –1] (C) (βˆ’βˆž,βˆ’2] (D) [–1, 1] f(π‘₯) = 2π‘₯3 + 9π‘₯2 + 12π‘₯ - 1 Calculating f’(𝒙) f’(π‘₯) = 6π‘₯2 +18π‘₯ + 12 - 0 f’(π‘₯) = 6(π‘₯2+3π‘₯+2) f’(π‘₯) = 6(π‘₯2+2π‘₯+π‘₯+2) f’(π‘₯) = 6(π‘₯(π‘₯+2)+1(π‘₯+2)) f’(𝒙) = 6(𝒙+𝟏) (𝒙+𝟐) Putting f’(𝒙) = 0 6(π‘₯+1) (π‘₯+2) = 0 (π‘₯+1) (π‘₯+2) = 0 So, 𝒙 = –1 , –2 Plotting points on number line Hence, f is decreasing for the interval (βˆ’2, βˆ’1). So, the correct answer is (B)

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