CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

CBSE Class 12 Sample Paper for 2021 Boards →
Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 26 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at May 29, 2023 by

The real function f (x) = 2x3 – 3x2 – 36x + 7 is:

(a) Strictly increasing in (−∞,−2) and strictly decreasing in ( −2, ∞)
(b) Strictly decreasing in (−2, 3)
(c) Strictly decreasing in (−∞, 3) and strictly increasing in (3, ∞)
(d) Strictly decreasing in (−∞,−2) ∪ (3, ∞)

 

This question is inspired from Ex 6.2, 5 - Chapter 6 Class 12 - Application of Derivatives

Slide66.JPG

Slide67.JPG
Slide68.JPG

This video is only available for Teachoo black users

Subscribe Now

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

Question 26 The real function f (x) = 2x3 – 3x2 – 36x + 7 is: (a) Strictly increasing in (−∞,−2) and strictly decreasing in ( −2, ∞) (b) Strictly decreasing in (−2, 3) (c) Strictly decreasing in (−∞, 3) and strictly increasing in (3, ∞) (d) Strictly decreasing in (−∞,−2) ∪ (3, ∞) f(𝑥) = 2𝑥3 – 3𝑥2 – 36𝑥 + 7 Calculating f’(𝒙) f’(𝑥) = 6𝑥2 – 6𝑥 – 36 + 0 f’(𝑥) = 6 (𝑥2 – 𝑥 – 6 ) f’(𝑥) = 6(𝑥^2 – 3𝑥 + 2𝑥 – 6) f’(𝑥) = 6(𝑥(𝑥 − 3) + 2 (𝑥 − 3)) f’(𝒙) = 6(𝒙 – 3) (𝒙 + 2) Putting f’(x) = 0 6(𝑥+2)(𝑥 –3)=0 (𝑥+2)(𝑥 –3)=0 So, x = −2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (−∞ ,−𝟐) & (𝟑 ,∞) f is strictly decreasing in (−𝟐, 𝟑) So, the correct answer is (D)

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.