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

Last updated at April 16, 2024 by

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(đ‘„) = 2đ‘„3 + 9đ‘„2 + 12đ‘„ - 1 is decreasing is: (A) [−1,∞) (B) [–2, –1] (C) (−∞,−2] (D) [–1, 1] f(đ‘„) = 2đ‘„3 + 9đ‘„2 + 12đ‘„ - 1 Calculating f’(𝒙) f’(đ‘„) = 6đ‘„2 +18đ‘„ + 12 - 0 f’(đ‘„) = 6(đ‘„2+3đ‘„+2) f’(đ‘„) = 6(đ‘„2+2đ‘„+đ‘„+2) f’(đ‘„) = 6(đ‘„(đ‘„+2)+1(đ‘„+2)) f’(𝒙) = 6(𝒙+𝟏) (𝒙+𝟐) Putting f’(𝒙) = 0 6(đ‘„+1) (đ‘„+2) = 0 (đ‘„+1) (đ‘„+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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