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

Last updated at Dec. 16, 2024 by Teachoo

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

Transcript

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)
  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise

    3. NCERT Exemplar - MCQs

    Tangents and Normals (using Differentiation) →
Tangents and Normals (using Differentiation) →
Chapter 6 Class 12 Application of Derivatives
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo