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

Transcript

Question 17 The interval on which the function f(๐‘ฅ) = 2๐‘ฅ3 + 9๐‘ฅ2 + 12๐‘ฅ - 1 is decreasing is: (A) [โˆ’1,โˆž) (B) [โ€“2, โ€“1] (C) (โˆ’โˆž,โˆ’2] (D) [โ€“1, 1] f(๐‘ฅ) = 2๐‘ฅ3 + 9๐‘ฅ2 + 12๐‘ฅ - 1 Calculating fโ€™(๐’™) fโ€™(๐‘ฅ) = 6๐‘ฅ2 +18๐‘ฅ + 12 - 0 fโ€™(๐‘ฅ) = 6(๐‘ฅ2+3๐‘ฅ+2) fโ€™(๐‘ฅ) = 6(๐‘ฅ2+2๐‘ฅ+๐‘ฅ+2) fโ€™(๐‘ฅ) = 6(๐‘ฅ(๐‘ฅ+2)+1(๐‘ฅ+2)) fโ€™(๐’™) = 6(๐’™+๐Ÿ) (๐’™+๐Ÿ) Putting fโ€™(๐’™) = 0 6(๐‘ฅ+1) (๐‘ฅ+2) = 0 (๐‘ฅ+1) (๐‘ฅ+2) = 0 So, ๐‘ฅ = โ€“1 , โ€“2 Plotting points on number line Hence, f is decreasing for the interval (โˆ’2, โˆ’1). So, the correct answer is (B)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.