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

Last updated at April 16, 2024 by

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

(A) [-1,∞)  

(B) [–2, –1]

(C) (-∞,-2]  

(D) [–1, 1]

 

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

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Question 4 The interval on which the function f(𝑥) = 2𝑥3 + 9𝑥2 + 12𝑥 - 1 is decreasing is: (A) [−1,∞) (B) [–2, –1] (C) (−∞,−2] (D) [–1, 1] f(𝑥) = 2𝑥3 + 9𝑥2 + 12𝑥 - 1 Calculating f’(𝒙) f’(𝑥) = 6𝑥2 +18𝑥 + 12 - 0 f’(𝑥) = 6(𝑥2+3𝑥+2) f’(𝑥) = 6(𝑥2+2𝑥+𝑥+2) f’(𝑥) = 6(𝑥(𝑥+2)+1(𝑥+2)) f’(𝒙) = 6(𝒙+𝟏) (𝒙+𝟐) Putting f’(𝒙) = 0 6(𝑥+1) (𝑥+2) = 0 (𝑥+1) (𝑥+2) = 0 So, 𝒙 = –1 , –2 Plotting points on number line Hence, f is decreasing for the interval (−2, −1). So, the correct answer is (B)

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