Check sibling questions

The interval on which the function f (x) =Β  2x 3 Β  + 9x 2 Β  + 12x - 1Β is decreasing is:

(A) [-1,∞)  

(B) [–2, –1]

(C) (-∞,-2]  

(D) [–1, 1]

Β 

This question is similar to Ex 6.2, 6 - Chapter 6 Class 12 - Application of Derivatives

Slide64.JPG
Slide65.JPG
Slide66.JPG

Get live Maths 1-on-1 Classs - Class 6 to 12


Transcript

Question 17 The interval on which the function f(π‘₯) = 2π‘₯3 + 9π‘₯2 + 12π‘₯ - 1 is decreasing is: (A) [βˆ’1,∞) (B) [–2, –1] (C) (βˆ’βˆž,βˆ’2] (D) [–1, 1] f(π‘₯) = 2π‘₯3 + 9π‘₯2 + 12π‘₯ - 1 Calculating f’(𝒙) f’(π‘₯) = 6π‘₯2 +18π‘₯ + 12 - 0 f’(π‘₯) = 6(π‘₯2+3π‘₯+2) f’(π‘₯) = 6(π‘₯2+2π‘₯+π‘₯+2) f’(π‘₯) = 6(π‘₯(π‘₯+2)+1(π‘₯+2)) f’(𝒙) = 6(𝒙+𝟏) (𝒙+𝟐) Putting f’(𝒙) = 0 6(π‘₯+1) (π‘₯+2) = 0 (π‘₯+1) (π‘₯+2) = 0 So, 𝒙 = –1 , –2 Plotting points on number line Hence, f is decreasing for the interval (βˆ’2, βˆ’1). So, the correct answer is (B)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.