The interval on which the function f (x) = 2x 3 + 9x 2 + 12x - 1 is decreasing is:
(A) [-1,â)
(B) [â2, â1]
(C) (-â,-2]
(D) [â1, 1]
This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives
NCERT Exemplar - MCQs
Last updated at Dec. 16, 2024 by Teachoo
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(đĽ) = 2đĽ3 + 9đĽ2 + 12đĽ - 1 is decreasing is: (A) [â1,â) (B) [â2, â1] (C) (ââ,â2] (D) [â1, 1] f(đĽ) = 2đĽ3 + 9đĽ2 + 12đĽ - 1 Calculating fâ(đ) fâ(đĽ) = 6đĽ2 +18đĽ + 12 - 0 fâ(đĽ) = 6(đĽ2+3đĽ+2) fâ(đĽ) = 6(đĽ2+2đĽ+đĽ+2) fâ(đĽ) = 6(đĽ(đĽ+2)+1(đĽ+2)) fâ(đ) = 6(đ+đ) (đ+đ) Putting fâ(đ) = 0 6(đĽ+1) (đĽ+2) = 0 (đĽ+1) (đĽ+2) = 0 So, đ = â1 , â2 Plotting points on number line Hence, f is decreasing for the interval (â2, â1). So, the correct answer is (B)