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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Last updated at April 16, 2024 by Teachoo
This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives
Question 4 The interval on which the function f(đ„) = 2đ„3 + 9đ„2 + 12đ„ - 1 is decreasing is: (A) [â1,â) (B) [â2, â1] (C) (ââ,â2] (D) [â1, 1] f(đ„) = 2đ„3 + 9đ„2 + 12đ„ - 1 Calculating fâ(đ) fâ(đ„) = 6đ„2 +18đ„ + 12 - 0 fâ(đ„) = 6(đ„2+3đ„+2) fâ(đ„) = 6(đ„2+2đ„+đ„+2) fâ(đ„) = 6(đ„(đ„+2)+1(đ„+2)) fâ(đ) = 6(đ+đ) (đ+đ) Putting fâ(đ) = 0 6(đ„+1) (đ„+2) = 0 (đ„+1) (đ„+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)