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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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)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.